{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0001","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"299dbbfc7f99fc722ea0bbd91d14fb61fc9c6d909744d1ab2a5ba9694e142bf9","family_id":"qf-density12-mapping-full-graph","seed":202610127001,"semantic_template":"qf-density12-mapping-full-graph/[]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is []."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0002","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c62fc1ab38a254b3f9b9e276372d08b27f370206cd47dbc32170b08ebea75ef","family_id":"qf-density12-mapping-full-graph","seed":202610127002,"semantic_template":"qf-density12-mapping-full-graph/[0]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(1)→Fin(1) has images=[0] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 0]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0003","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b31bd5a5ff750d242df6279049c2e815478bb35a4042eef9ee24861ae2cf6a69","family_id":"qf-density12-mapping-full-graph","seed":202610127003,"semantic_template":"qf-density12-mapping-full-graph/[2,0,5]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[2, 0, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 2], [1, 0], [2, 5]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 2], [1, 0], [2, 5]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0004","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ebfb6383927ab36c7e42e89646fe641d68bc4f8a683be5729ffb23ab6e7d911","family_id":"qf-density12-mapping-full-graph","seed":202610127004,"semantic_template":"qf-density12-mapping-full-graph/[3,0,6]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[3, 0, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 3], [1, 0], [2, 6]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 3], [1, 0], [2, 6]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0005","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2381d709f7010bb5eafdfdf0851ec3d8559153b4968beb689e26f5f7e1803193","family_id":"qf-density12-mapping-full-graph","seed":202610127005,"semantic_template":"qf-density12-mapping-full-graph/[4,0,7]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[4, 0, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 4], [1, 0], [2, 7]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 4], [1, 0], [2, 7]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0006","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dda312450c8a5a07435db62ff66885cee47d0eef8d29d6b9cd905c9a1d83fde5","family_id":"qf-density12-mapping-full-graph","seed":202610127006,"semantic_template":"qf-density12-mapping-full-graph/[5,0,0]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[5, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 5], [1, 0], [2, 0]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 5], [1, 0], [2, 0]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0007","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e06f07bcbd1ec849d26a1374b1e8022a860be978a91155b0a0e0c65d75dd232b","family_id":"qf-density12-mapping-full-graph","seed":202610127007,"semantic_template":"qf-density12-mapping-full-graph/[6,0,1]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[6, 0, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 6], [1, 0], [2, 1]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 6], [1, 0], [2, 1]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0008","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23ecbe53521d92ee986b936a8f38faf90de34d4d6b03b272b008533a9f30f2dd","family_id":"qf-density12-mapping-full-graph","seed":202610127008,"semantic_template":"qf-density12-mapping-full-graph/[7,0,2]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[7, 0, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 7], [1, 0], [2, 2]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 7], [1, 0], [2, 2]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0009","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7033e209d73d49386f27fd72943c3ea1fcf5ad4438cb1e87bede6624b01eedec","family_id":"qf-density12-mapping-full-graph","seed":202610127009,"semantic_template":"qf-density12-mapping-full-graph/[0,1,3]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 0], [1, 1], [2, 3]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0], [1, 1], [2, 3]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0010","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"432e46c2d5115de22d25b719adf15fc6dbf8286c5fbf96f2aaf957145d456342","family_id":"qf-density12-mapping-full-graph","seed":202610127010,"semantic_template":"qf-density12-mapping-full-graph/[1,1,4]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[1, 1, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 1], [1, 1], [2, 4]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 1], [1, 1], [2, 4]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0011","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18edebe206a3247ce69c7785d7764740333af0c897078dac7b05705687a01c3e","family_id":"qf-density12-mapping-full-graph","seed":202610127011,"semantic_template":"qf-density12-mapping-full-graph/[2,1,5]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[2, 1, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 2], [1, 1], [2, 5]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 2], [1, 1], [2, 5]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0012","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee02faca8605edd7f6a00bc6521653fa3642e380c7398a02b7a494694bd1de32","family_id":"qf-density12-mapping-full-graph","seed":202610127012,"semantic_template":"qf-density12-mapping-full-graph/[3,1,6]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[3, 1, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 3], [1, 1], [2, 6]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 3], [1, 1], [2, 6]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0013","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad6e0cda64af6db4aa906c253c56392d2d6579c7d97fd885b2da92b60fa725cb","family_id":"qf-density12-mapping-full-graph","seed":202610127013,"semantic_template":"qf-density12-mapping-full-graph/[4,1,7]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[4, 1, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 4], [1, 1], [2, 7]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 4], [1, 1], [2, 7]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0014","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb7dbf649b158a2edde661f3acef31fa59309116d8883a52f3a306b54bb497d1","family_id":"qf-density12-mapping-full-graph","seed":202610127014,"semantic_template":"qf-density12-mapping-full-graph/[5,1,0]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[5, 1, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 5], [1, 1], [2, 0]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 5], [1, 1], [2, 0]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0015","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e747b8a7f9fcb22478e504a4581da2de37475728a0a9f4ee8ada08b3f13fbcdd","family_id":"qf-density12-mapping-full-graph","seed":202610127015,"semantic_template":"qf-density12-mapping-full-graph/[6,1,1]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[6, 1, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 6], [1, 1], [2, 1]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 6], [1, 1], [2, 1]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0016","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04eb16f14806dfaa6c0db2f5ed8d4f3823098c784578616b2c88d549d259272b","family_id":"qf-density12-mapping-full-graph","seed":202610127016,"semantic_template":"qf-density12-mapping-full-graph/[7,1,2]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[7, 1, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 7], [1, 1], [2, 2]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 7], [1, 1], [2, 2]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0017","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54cdd5a5a144d194c4753a9a1c29f1f7cfcd142504005c8fafa6a43803e891c3","family_id":"qf-density12-mapping-full-graph","seed":202610127017,"semantic_template":"qf-density12-mapping-full-graph/[0,2,3]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 0], [1, 2], [2, 3]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0], [1, 2], [2, 3]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0018","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ebe6dd70b8a8efcc5943fec22e1be69b82cb2e888bd7294fecc86731acbd16b1","family_id":"qf-density12-mapping-full-graph","seed":202610127018,"semantic_template":"qf-density12-mapping-full-graph/[1,2,4]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[1, 2, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 1], [1, 2], [2, 4]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 1], [1, 2], [2, 4]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0019","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"58da9e4792903569772c566b3a326cf3451069b6ed26421bae494ad9906e8c11","family_id":"qf-density12-mapping-full-graph","seed":202610127019,"semantic_template":"qf-density12-mapping-full-graph/[2,2,5]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[2, 2, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 2], [1, 2], [2, 5]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 2], [1, 2], [2, 5]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0020","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c171c4287c96dda3870fcf0b1f4076ca833fa65a2c7243c6899750d12554886","family_id":"qf-density12-mapping-full-graph","seed":202610127020,"semantic_template":"qf-density12-mapping-full-graph/[3,2,6]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[3, 2, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 3], [1, 2], [2, 6]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 3], [1, 2], [2, 6]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0021","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"824e67bfec38c011bd26d04c2dab6246ed0c89bff957d568dd4735d2a8899c9d","family_id":"qf-density12-mapping-full-graph","seed":202610127021,"semantic_template":"qf-density12-mapping-full-graph/[4,2,7]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[4, 2, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 4], [1, 2], [2, 7]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 4], [1, 2], [2, 7]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0022","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"17b6faf27af8e9a393ec75fc1220f426815cbd1362eb4a3c38ceccb9fc44032e","family_id":"qf-density12-mapping-full-graph","seed":202610127022,"semantic_template":"qf-density12-mapping-full-graph/[5,2,0]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[5, 2, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 5], [1, 2], [2, 0]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 5], [1, 2], [2, 0]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0023","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"540b0ff81d6f862de9d23d73f1023a5a118a589e908729477b0cb943e0a66f53","family_id":"qf-density12-mapping-full-graph","seed":202610127023,"semantic_template":"qf-density12-mapping-full-graph/[6,2,1]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[6, 2, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 6], [1, 2], [2, 1]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 6], [1, 2], [2, 1]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0024","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce2cf543350776b9c1732a47ec4ea134097db46ac7ec42f8d2365367dba7fce6","family_id":"qf-density12-mapping-full-graph","seed":202610127024,"semantic_template":"qf-density12-mapping-full-graph/[7,2,2]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[7, 2, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 7], [1, 2], [2, 2]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 7], [1, 2], [2, 2]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0025","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"10303db94d17ba157d18466ca8d3513906d254d18d11a8bc4b99672f868c8acc","family_id":"qf-density12-mapping-full-graph","seed":202610127025,"semantic_template":"qf-density12-mapping-full-graph/[0,3,3]"},"fields":{"title":"Complete Ordered Finite Mapping Graph","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 3, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.","answer":{"kind":"expression","value":"[[0, 0], [1, 3], [2, 3]]","explanation":"Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0], [1, 3], [2, 3]]."},"skills":["Complete Ordered Finite Mapping Graph"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0026","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8674aa41437448a0f9dcf870eefbcef438e11dc9dad185ca81f1ceb427fb0769","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127026,"semantic_template":"qf-density12-mapping-range-codomain-defect/[0,[]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([], [], Yes)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([], [], Yes)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0027","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c56d311d11700d6f7696cdf9599f37d76d808ad78a05915610e05e10d5ea7648","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127027,"semantic_template":"qf-density12-mapping-range-codomain-defect/[1,[]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(0)→Fin(1) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([], [0], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([], [0], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0028","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ea2b643ba0660dfcf8efb0a2d76da62ff4f43e2795650d448c9a421fa21efdf","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127028,"semantic_template":"qf-density12-mapping-range-codomain-defect/[2,[0,1]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 1], [], Yes)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1], [], Yes)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0029","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffeabb8bf09256e22a65fc357a4ca98c127b66b78e66eeef4fc89e753d612060","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127029,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(1)→Fin(8) has images=[0] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0], [1, 2, 3, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0], [1, 2, 3, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0030","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28441ea01187dca0e1e9406db4388c49fbee066cfa7fb3ad961b6deda2ca31db","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127030,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[1]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(1)→Fin(8) has images=[1] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([1], [0, 2, 3, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1], [0, 2, 3, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0031","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c9cae66029391e09129e46fad5a3dac443b5e71f4cf829978e6d3cf89fad97e","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127031,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,1]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 1], [2, 3, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1], [2, 3, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0032","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f2f55efeae91e90eda2f43fb12a44ca987c37e7e8af475891498383666535812","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127032,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[2]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(1)→Fin(8) has images=[2] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([2], [0, 1, 3, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([2], [0, 1, 3, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0033","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07de599f9fa04a5f4816241816b5033d5fe657298d0ad3e1b8ffc83b34b806ad","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127033,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,2]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[0, 2] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 2], [1, 3, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 2], [1, 3, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0034","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2499f497611841f05402892fd263ffefdd8bcef11a268922ead240de4473737f","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127034,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[1,2]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[1, 2] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([1, 2], [0, 3, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 2], [0, 3, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0035","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d8bd097d45136b8c7ea7c871993ed5b3cac2d8b6c6a04b27f2b43ffaf6359f2","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127035,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,1,2]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 1, 2], [3, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 2], [3, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0036","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9525da98f2ed4552b0be53895f9d2a448cee340707eda7a08f02e5d74947b100","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127036,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(1)→Fin(8) has images=[3] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([3], [0, 1, 2, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([3], [0, 1, 2, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0037","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87e6534874fd0b00b89d3da84878a35eca43905f7f7150d454c2b06d8cb564f1","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127037,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[0, 3] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 3], [1, 2, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 3], [1, 2, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0038","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"168814bc5e85716e668f4083f7abd6a950544e6fd274639766e571ba5c3b0912","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127038,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[1,3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[1, 3] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([1, 3], [0, 2, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 3], [0, 2, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0039","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"afa44f0c51446031094f5f2f9435a71f4f494d35b972e613b928e6cc299562ee","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127039,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,1,3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 1, 3], [2, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 3], [2, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0040","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66fc3649845c4d858cd88879cda5784d0e1582ebfb2c0d41bcad417cec8683c3","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127040,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[2,3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[2, 3] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([2, 3], [0, 1, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([2, 3], [0, 1, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0041","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"206045f93e1194a3f76c4a19c6e495c329c24f73fb0b0dd26a7f46ab889e4b62","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127041,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,2,3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 2, 3], [1, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 2, 3], [1, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0042","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d88523b59ccd42eef564baaf6a3936fcf89ba691c0f3b10b2974824cf248f9a","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127042,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[1,2,3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(3)→Fin(8) has images=[1, 2, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([1, 2, 3], [0, 4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 2, 3], [0, 4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0043","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b26e457c068b651493b95392e82eb4129b93893803800de761fdf196153a381","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127043,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,1,2,3]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(4)→Fin(8) has images=[0, 1, 2, 3] indexed from 0; Fin(4)={0,…,3}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 1, 2, 3], [4, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 2, 3], [4, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0044","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0fda83339b38d3437c7bcbf0c1c61062569d1d74533711cf51a215d9892b96a","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127044,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[4]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(1)→Fin(8) has images=[4] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([4], [0, 1, 2, 3, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([4], [0, 1, 2, 3, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0045","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"256afa1c066025396dd76407776c84619c993177b418817663a45e17e6255439","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127045,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,4]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[0, 4] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 4], [1, 2, 3, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 4], [1, 2, 3, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0046","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d77e1db386c980d7bc164c47e3769896d10e3b359d3ba0a0d9472bab83e13af","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127046,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[1,4]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[1, 4] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([1, 4], [0, 2, 3, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 4], [0, 2, 3, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0047","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cce0373542aaeaa7105a63401ab297870c0bee9020f497b8cc03056e7fd7e92a","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127047,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,1,4]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 1, 4], [2, 3, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 4], [2, 3, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0048","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1bd6d003452b541177e4e700e5995705cce0d1045b71e410f6213bd3aa5ca35","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127048,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[2,4]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(2)→Fin(8) has images=[2, 4] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([2, 4], [0, 1, 3, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([2, 4], [0, 1, 3, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0049","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ea0c0c301f7cfafba0d9b9e10cff075e47974ef7ed1c8d11867652c1607de17","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127049,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,2,4]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([0, 2, 4], [1, 3, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 2, 4], [1, 3, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0050","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"608c4dcd7fb59afdb720ac7edb777721d185ae8d8af0abac06804945d86b9726","family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127050,"semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[1,2,4]]"},"fields":{"title":"Actual Range and Unused Codomain","stem":"The complete total map f:Fin(3)→Fin(8) has images=[1, 2, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).","answer":{"kind":"expression","value":"([1, 2, 4], [0, 3, 5, 6, 7], No)","explanation":"Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 2, 4], [0, 3, 5, 6, 7], No)."},"skills":["Actual Range and Unused Codomain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0051","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf5bdc328439f5bc42693cac9e7dec5e38c8cae73fa8ce4b5961414fb86aab3b","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127051,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"untyped\"],[\"untyped\"]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. Ordered queries=[-1, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, No, No], [ill-typed, ill-typed, ill-typed])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, No, No], [ill-typed, ill-typed, ill-typed])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0052","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"15658de743323335d6161adb2a860b9d0089e613015ef6ecbbcb66454a0328d8","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127052,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"untyped\"],[\"untyped\"]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 101, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, No, No], [1, ill-typed, ill-typed])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, No], [1, ill-typed, ill-typed])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0053","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ece7b90d40a56556f18c8a9c9dd9cfcc256c9590f192eb5e10ba39906c30159","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127053,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"typed\",0],[\"untyped\"]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 0, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, No], [0, 0, ill-typed])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [0, 0, ill-typed])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0054","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0654b0c26eca0647f0b9556f8a86d157458e6ea1a57bf5ef0f152d0f8ddf14d","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127054,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"typed\",0],[\"untyped\"]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 0, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, No], [1, 0, ill-typed])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [1, 0, ill-typed])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0055","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b2b0533737d75aa4dac2de1e8fbbdc23c3240af0d9d43ceccfa2cd5543db64c7","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127055,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"typed\",1],[\"untyped\"]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 1, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, Yes, No], [ill-typed, 1, ill-typed])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, No], [ill-typed, 1, ill-typed])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0056","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6cd17d2ac8ac3e3d35a57ccb1dae2190e197896d84d7915df9e2b430f86c8ebe","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127056,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"typed\",1],[\"untyped\"]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 1, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, No], [0, 1, ill-typed])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [0, 1, ill-typed])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0057","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"473af04575e3dc2b8581c4d75e73d87b5259386aab0e39eaa69b954ab7b4b0e5","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127057,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"typed\",1],[\"untyped\"]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 1, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, No], [1, 1, ill-typed])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [1, 1, ill-typed])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0058","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf00133ee9febe23ee3b3d807afdcfb2e490f4887027f558744b444b8d81895f","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127058,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"untyped\"],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 101, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, No, Yes], [ill-typed, ill-typed, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, No, Yes], [ill-typed, ill-typed, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0059","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b292c9b7afc54f9b745da76285b1261ed6cc6af8172369b71ead02b5ed26b3fc","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127059,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"untyped\"],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 101, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, No, Yes], [0, ill-typed, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [0, ill-typed, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0060","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc544eaedee36d37f693e6f60b2b6e8322e968fc172cee561eb8de6bd2ac47a5","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127060,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"untyped\"],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 101, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, No, Yes], [1, ill-typed, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [1, ill-typed, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0061","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"79cb0ea9d71099da30f7cef091d50b26faf750ea1133b70244807fa0c5ece593","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127061,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"typed\",0],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 0, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, Yes, Yes], [ill-typed, 0, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 0, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0062","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ea283579bf423f6933dd6a940daef9db560129c6a5cf20ef0a4b8db904a0c01","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127062,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"typed\",0],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 0, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [0, 0, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 0, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0063","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"27bb7adc6bea8796a05f78489e738d8c9dbcc11cf118054f5c2998f899f7ab42","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127063,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"typed\",0],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 0, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [1, 0, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 0, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0064","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f86e69654a51ffcf997c85fee38f95d025b96eb8e2f05fe02c4173e5f6f76be","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127064,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"typed\",1],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 1, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, Yes, Yes], [ill-typed, 1, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 1, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0065","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ce1eb3d49e029b6dd2529190bd6c064314e1b51b550e2ffb64149d9d275ebde","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127065,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"typed\",1],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 1, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [0, 1, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 1, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0066","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6a04469009f6f2a3169c996b57f48f1051c47230022a4d24854d2c020664e84","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127066,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"typed\",1],[\"typed\",0]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 1, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [1, 1, 0])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 1, 0])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0067","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e1be689724d27206246105c4a72c8d845d9fb106d5d9a57eedea1d3822855da","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127067,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"untyped\"],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 101, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, No, Yes], [ill-typed, ill-typed, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, No, Yes], [ill-typed, ill-typed, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0068","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae4668eb334a27bb8fdff8537c2c66e14db08a09425db90bc0e5f43db3422b4b","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127068,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"untyped\"],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 101, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, No, Yes], [0, ill-typed, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [0, ill-typed, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0069","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2dc11458f4987128f3eb6abe656129a8475b218d5c7c29d4faef466fe96f5a11","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127069,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"untyped\"],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 101, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, No, Yes], [1, ill-typed, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [1, ill-typed, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0070","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3345f3a67398f11b55923a0c1e982fba3ce2832613cd0c878b248c912bc3904","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127070,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"typed\",0],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, Yes, Yes], [ill-typed, 0, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 0, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0071","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"777b9867632b4210ba486849f9ca50a9c3557351ddf7432c815a0360fd4261f3","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127071,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"typed\",0],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [0, 0, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 0, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0072","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b35ee43773984a942a6157e2f49deb3d52947e7e8fd59cc8dfaaf1947b37fe3","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127072,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"typed\",0],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [1, 0, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 0, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0073","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2973ad9bd6be5b17b28b5b6ec8ddee3f12ba5370a23a5da9741f842f74c7a55","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127073,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"untyped\"],[\"typed\",1],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 1, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([No, Yes, Yes], [ill-typed, 1, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 1, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0074","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5004de083b191796643ae79422ba16d36d9d4cc165442cac97e3cd22b35b0bd4","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127074,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",0],[\"typed\",1],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 1, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [0, 1, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 1, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0075","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b716196b0ab51b018301bf1872e684083bf7b5d1c97520924f51a8b88637f716","family_id":"qf-density12-mapping-candidate-evaluation","seed":202610127075,"semantic_template":"qf-density12-mapping-candidate-evaluation/[[\"typed\",1],[\"typed\",1],[\"typed\",1]]"},"fields":{"title":"Typed Candidate Evaluation of a Total Map","stem":"The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 1, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.","answer":{"kind":"expression","value":"([Yes, Yes, Yes], [1, 1, 1])","explanation":"Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 1, 1])."},"skills":["Typed Candidate Evaluation of a Total Map"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0076","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd0f74410bf1648a28eb23578be9eca91bde28fa4d0b5db04d9ea77b7362467e","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127076,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. A second complete total map g on the same types has other=[]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([], [])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([], [])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0077","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a98cc4aded64daa695fca9c18beb39ca46d01ab0cbdd2148d7c54b3c15fe67d","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127077,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,0,1]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[1, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[0, 1]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[0, 1]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0078","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7c4211d12bbc790fb3cfc10fdf059165fb41fab6e9b642fa21f04ecdfbd2685","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127078,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,0,1]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 1, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[0, 1]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[0, 1]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0079","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"397a8b07fed995e704415b64c98a5f0c3b7a65fc73d17a002718b05c1ea26fef","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127079,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,0,1]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 1]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[0, 1]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[0, 1]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0080","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"84a91c21bbc138d9d1e59dfddd7e7152a6ef1e29c9dbf5c07cda77e63f06e746","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127080,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,1,2]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[1, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[2, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[1, 2]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[1, 2]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0081","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5806a7d90c8032735c5268c4382a2dd843e2b46839c3443fe2f3d537d898afc4","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127081,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,1,2]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 2, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[1, 2]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[1, 2]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0082","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a83fd5df1d0d3b6445f8002b6a6158b974a95edfbcb7a54b9de4bc3671f4f4f6","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127082,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,1,2]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 2]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[1, 2]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[1, 2]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0083","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8b5dffcca040c634d42a7e9244b6b5a9e35738c994c6d5a20ab6be72a4682675","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127083,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,2,3]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[2, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[3, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[2, 3]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[2, 3]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0084","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25c276745cb1119907f9e057420524f4ffda70c4fd6bb9b73fac3e9217db1678","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127084,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,2,3]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 3, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[2, 3]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[2, 3]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0085","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"43808da03686000a082443acc9da238721c85e54e87d643647f1d5438acec3cc","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127085,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,2,3]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 3]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[2, 3]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[2, 3]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0086","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ad1390676d18fbeb090cb48b901415b4e0835e606c535abe0c0bc5c247e95cc","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127086,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,3,4]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[3, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[4, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[3, 4]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[3, 4]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0087","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"47997bbdf376b36ba061e69b889b13d4cb5f2a341ef75f7d84999bec1fba0a7a","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127087,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,3,4]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 3, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 4, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[3, 4]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[3, 4]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0088","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"809926d15f4eaf4052bffcd8a95aa54b36de7aefd45d8cbc14f5dcfacd61769c","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127088,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,3,4]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 4]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[3, 4]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[3, 4]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0089","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"054afe4c8ffd6ae68bd720b7eb7c69e29f60ccfe98872827084cfcaf30ff8d15","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127089,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,4,5]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[4, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[5, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[4, 5]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[4, 5]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0090","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b1a104598a74578d02a7462802b5b15aed2fb7a004365eb2b051c54597898ef","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127090,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,4,5]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 4, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 5, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[4, 5]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[4, 5]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0091","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"824bdc63c7479f4a2243affee370cfc3c4d9bc81f4df87f570ec884de4946b75","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127091,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,4,5]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 5]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[4, 5]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[4, 5]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0092","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4806fd01dc12cb202f643b113c66df1ab42c9a8b9043a673a3540e6522e6dfcf","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127092,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,5,6]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[5, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[6, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[5, 6]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[5, 6]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0093","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"809c501203135bafe0292572275dc3244ba3b09c49b805a20af6d9c3d88464c0","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127093,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,5,6]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 5, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 6, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[5, 6]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[5, 6]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0094","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ded0c18d24f6a51a3abfa0faeb30a08fd1d124a5b163d02f0a8cd2ebdb73d3c","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127094,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,5,6]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 6]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[5, 6]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[5, 6]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0095","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cae2ef42dcd3a6728b6abd560ce6092f578cd2c9361b39ea4ac48b0b8ec88748","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127095,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,6,7]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[6, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[7, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[6, 7]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[6, 7]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0096","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb91eec0819da287d5ad98762d5016977ccb2a3cf5968c2e94128b196d7cec07","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127096,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,6,7]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 6, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 7, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[6, 7]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[6, 7]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0097","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"47cd931bb3892df2d99a5dea07d79b6db061d7aef6e79f17ba87d9d65471054e","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127097,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,6,7]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 7]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[6, 7]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[6, 7]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0098","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4dd889c820a032ef413879a5d07b5f1842ca64f510bc714c329de74f02a28324","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127098,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[0,7,0]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[7, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([0], [[7, 0]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[7, 0]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0099","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"403d30942ecac97a43f8b6d052ffb9dde4b772ee6510018aaeb907d140777a13","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127099,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[1,7,0]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 7, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([1], [[7, 0]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[7, 0]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r07-function-mapping-0100","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b089f54f86157b04df0668b054f35daa4ae1bcaffda66ab10761f4ee45f25145","family_id":"qf-density12-mapping-equality-obstruction-list","seed":202610127100,"semantic_template":"qf-density12-mapping-equality-obstruction-list/[[2,7,0]]"},"fields":{"title":"Complete Mapping Mismatch Indices and Ordered Values","stem":"The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).","answer":{"kind":"expression","value":"([2], [[7, 0]])","explanation":"Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[7, 0]])."},"skills":["Complete Mapping Mismatch Indices and Ordered Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}