{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0001","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee55dfe058504dca1327b24b06c9b32593d89cd77896d510694257edc464b939","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153001,"semantic_template":"qf-density15-typed-domain-range-inventory/[0,0,[]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(0)=∅ is the source and Fin(0)=∅ the codomain; complete typed images=[] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([0, 0], [], [], [], 0)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([0, 0], [], [], [], 0)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0002","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63137128d7e4b4a8427679fde26fb5cf69a467deec1ada481b7ddcfdcdecc0ca","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153002,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,0,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0], [2, 0]], [0], [1, 2], 1)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 0], [2, 0]], [0], [1, 2], 1)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0003","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9aeffa9d7081e915210056a96bbac79ce56e8e70f386c75f8742391ccdbdb8f","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153003,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,0,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0], [2, 0]], [0, 1], [2], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 0], [2, 0]], [0, 1], [2], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0004","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8c8ac9b71bb01a621b5a4be1ed61221b85ad0d5076423bdffc9bf03af88f3db","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153004,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,0,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0], [2, 0]], [0, 2], [1], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 0], [2, 0]], [0, 2], [1], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0005","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68dfd7ee540fdd37199403e40718f361624870e604be5a1885c0520a114a264d","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153005,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,1,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1], [2, 0]], [0, 1], [2], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 1], [2, 0]], [0, 1], [2], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0006","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5ae34e63b2e87b4b54f47c2bf3c0878041703c58890e99fc4e63b6a5254ad2b2","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153006,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,1,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1], [2, 0]], [0, 1], [2], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 1], [2, 0]], [0, 1], [2], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0007","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"332ae544fa8206696987bb1bd5e0497eed7059023173c0e8d186bbdfa6481818","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153007,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,1,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1], [2, 0]], [0, 1, 2], [], 3)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 1], [2, 0]], [0, 1, 2], [], 3)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0008","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"213b8272ef98c1846f1b78005a06513dd5e0f5a7ce75b213a92c3f58b2bf768f","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153008,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,2,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 2, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 2], [2, 0]], [0, 2], [1], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 2], [2, 0]], [0, 2], [1], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0009","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54ad9e76e5bc1ea86b77cd561fc92488e01cc48d963c46dc87726d924e1ba67b","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153009,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,2,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 2, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 2], [2, 0]], [0, 1, 2], [], 3)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 2], [2, 0]], [0, 1, 2], [], 3)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0010","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6fd019bd11168c3de03de812a1c7e3de3117f8af6a4979d6ec018cd47c135e3a","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153010,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,2,0]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 2, 0] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 2], [2, 0]], [0, 2], [1], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 2], [2, 0]], [0, 2], [1], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0011","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5759e7d022162f0ff49055c20f45de40773d20b5da37fc40689d760c3d838e84","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153011,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,0,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0], [2, 1]], [0, 1], [2], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 0], [2, 1]], [0, 1], [2], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0012","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc61677dc0d1260d0f449cf630e81c282b27f9a53d9e45befdf36b547fc7b71b","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153012,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,0,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0], [2, 1]], [0, 1], [2], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 0], [2, 1]], [0, 1], [2], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0013","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"759fee10e595c2216b2100c85d15cf8b62a595e09ad4ebc30214f8c42fad2acb","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153013,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,0,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0], [2, 1]], [0, 1, 2], [], 3)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 0], [2, 1]], [0, 1, 2], [], 3)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0014","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"401a894cc1c656461e6f0cc8ebb0ed1490f8e89b7ee4d84bbce69abce7cb0b96","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153014,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,1,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1], [2, 1]], [0, 1], [2], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 1], [2, 1]], [0, 1], [2], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0015","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd46759ab127397e56888fa10e0f9a3710c26740763c7289f596df0c297f3351","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153015,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,1,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1], [2, 1]], [1], [0, 2], 1)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 1], [2, 1]], [1], [0, 2], 1)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0016","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7090369baa9048b2d7586903a03e33f296d9d8f6efb4c1719a87f729c9ce05cb","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153016,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,1,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 1, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1], [2, 1]], [1, 2], [0], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 1], [2, 1]], [1, 2], [0], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0017","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f211c6a15a07a0cc5ac591f531f1957c48a1cf52cd665910442508f124c467ca","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153017,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,2,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 2, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 2], [2, 1]], [0, 1, 2], [], 3)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 2], [2, 1]], [0, 1, 2], [], 3)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0018","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aab882740c31602ff6f7ab40f2db5510f553e9c063c699e0d371f1433bb2c4e1","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153018,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,2,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 2, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 2], [2, 1]], [1, 2], [0], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 2], [2, 1]], [1, 2], [0], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0019","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e71f3c7596695f57ae10c58194088edf0f0c808dfed068181ef9e1ab49f06391","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153019,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,2,1]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 2, 1] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 2], [2, 1]], [1, 2], [0], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 2], [2, 1]], [1, 2], [0], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0020","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b1bb32a305a70ad5317d60523a7dc26b3bc8b9fe03750e82a3047bb0669dc69","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153020,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,0,2]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 2] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0], [2, 2]], [0, 2], [1], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 0], [2, 2]], [0, 2], [1], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0021","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68ffba87819a0baea2d88def41371604fc9b5cbc925025171d30eef200b6329f","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153021,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,0,2]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 2] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0], [2, 2]], [0, 1, 2], [], 3)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 0], [2, 2]], [0, 1, 2], [], 3)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0022","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4247dae5fd8840f77c109c05dd07f81fa134cdcd287d17822f5dbcfd2f2016d","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153022,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,0,2]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 0, 2] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0], [2, 2]], [0, 2], [1], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 0], [2, 2]], [0, 2], [1], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0023","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81c17da13394e6930b2dfd7349daa6209dcc63d99f8d4c067f199235f7aa3f96","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153023,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,1,2]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 2] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1], [2, 2]], [0, 1, 2], [], 3)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 0], [1, 1], [2, 2]], [0, 1, 2], [], 3)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0024","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c61a5b5b626cf34a1cbbbd13b0847e1a95395d14dfa16af9ca3d43771f9252aa","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153024,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,1,2]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 2] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1], [2, 2]], [1, 2], [0], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 1], [1, 1], [2, 2]], [1, 2], [0], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0025","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6f05553d7fe24d198a063e3e1d53077ea12c05e68af195ac611fca4d4d0ff90","family_id":"qf-density15-typed-domain-range-inventory","seed":202610153025,"semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,1,2]]"},"fields":{"title":"Complete Domain, Codomain, Graph, and Range Inventory","stem":"Fin(3)={0,…,2} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[2, 1, 2] are indexed from 0. All entries must be typed, even unused ones. Give ([n,m], all ordered [x,images[x]] rows, increasing range, unused codomain, range size).","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1], [2, 2]], [1, 2], [0], 2)","explanation":"Read every source output; deduplicate outputs for the range and subtract from the codomain. A total mathematical table is not a partial program function. The exact result, retaining the requested order, is ([3, 3], [[0, 2], [1, 1], [2, 2]], [1, 2], [0], 2)."},"skills":["Complete Domain, Codomain, Graph, and Range Inventory"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0026","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"288d9d38fb9841f04fb9ac191c939ac9562c92d17856da35a9ed06e972b9f4ef","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153026,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"untyped\"],[\"untyped\"]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(0)=∅ is the source and Fin(0)=∅ the codomain; complete typed images=[] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, -1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([No, No], [outside-codomain, outside-codomain], [outside-codomain, outside-codomain])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([No, No], [outside-codomain, outside-codomain], [outside-codomain, outside-codomain])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0027","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4d0e090c088db91537e89e941f44b6025988c9e017323ba926e9530497104ec","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153027,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[]],[\"typed\",[]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(0)=∅ is the source and Fin(2)={0,…,1} the codomain; complete typed images=[] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[], []], [0, 0])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[], []], [0, 0])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0028","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1242f61c660519504fbd20f01beca4f16868e6a1e6cf0b712976ff34d7e667b","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153028,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"untyped\"],[\"typed\",[0,2]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(3)={0,…,2} is the source and Fin(2)={0,…,1} the codomain; complete typed images=[0, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[2, 0]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([No, Yes], [outside-codomain, [0, 2]], [outside-codomain, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([No, Yes], [outside-codomain, [0, 2]], [outside-codomain, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0029","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"989d57eba74c7a3e5db3bfd756de1baabf38b3681f437e35f16df82489ca4ece","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153029,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,2,3,4]],[\"typed\",[]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 0, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 1, 2, 3, 4], []], [5, 0])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 1, 2, 3, 4], []], [5, 0])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0030","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8f062d72cc2c0a6ba20d6ce709421ffd598b603afc9a1225e5094f65efa6d979","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153030,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,2,3,4]],[\"typed\",[0]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 0, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[1, 2, 3, 4], [0]], [4, 1])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[1, 2, 3, 4], [0]], [4, 1])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0031","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74fb2e86a50af94dd1c745e88548be6af196a7a93b3178b98f2ed0163580d468","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153031,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,2,3,4]],[\"typed\",[1]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 0, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 2, 3, 4], [1]], [4, 1])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 2, 3, 4], [1]], [4, 1])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0032","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a487eeb5d1cec1d4ed3c537ce6eec769472108e2af7f185307549ed857a164b","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153032,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[2,3,4]],[\"typed\",[0,1]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 0, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[2, 3, 4], [0, 1]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[2, 3, 4], [0, 1]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0033","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f99d7e9709b90a7edaa8caa73a57208dd23addc3dca00905aa55482a25417c6","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153033,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,3,4]],[\"typed\",[2]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 1, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 1, 3, 4], [2]], [4, 1])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 1, 3, 4], [2]], [4, 1])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0034","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"43fb4f5ba40488ebb382d8e6bb9fc05f124aefdb942383aa42594b96c0ca9e29","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153034,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,3,4]],[\"typed\",[0,2]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 1, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[1, 3, 4], [0, 2]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[1, 3, 4], [0, 2]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0035","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e6d79513c553b17c18589847fc84ebd0872e8497760562bf72479b14100ba05","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153035,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,3,4]],[\"typed\",[1,2]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 1, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 3, 4], [1, 2]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 3, 4], [1, 2]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0036","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf814cacb0259dbace41c4da5d7e38831573989af52c38eb038827be67db0706","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153036,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[3,4]],[\"typed\",[0,1,2]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 1, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[3, 4], [0, 1, 2]], [2, 3])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[3, 4], [0, 1, 2]], [2, 3])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0037","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"115c5a79a717199d11cef4b92ac37710c873dea241fb6365d4556ef35215ae5a","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153037,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,2,4]],[\"typed\",[3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 0, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 1, 2, 4], [3]], [4, 1])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 1, 2, 4], [3]], [4, 1])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0038","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7102c2ab93dcadfaa9924992bf328a816bf4cc8562a76929e40fa6674ec647c5","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153038,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,2,4]],[\"typed\",[0,3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 0, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[1, 2, 4], [0, 3]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[1, 2, 4], [0, 3]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0039","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4d792bf7ea2f2f1ddd9b23a761c633444eea42001b21743731de4ca0cff47d4","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153039,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,2,4]],[\"typed\",[1,3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 0, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 2, 4], [1, 3]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 2, 4], [1, 3]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0040","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9eee6f78415b992a64780391bd56fc26433ba68f4b991f5c5ac7aa17155a06e7","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153040,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[2,4]],[\"typed\",[0,1,3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 0, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[2, 4], [0, 1, 3]], [2, 3])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[2, 4], [0, 1, 3]], [2, 3])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0041","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c71d699271ce019c4c321eccda1796f62795dc6ea89381cd2a676dbe8e03a4a","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153041,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,4]],[\"typed\",[2,3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 1, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 1, 4], [2, 3]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 1, 4], [2, 3]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0042","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b056c5b2fd4e3c81a026b046f9d32c8f55202ec2870d55454a5346685709070","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153042,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,4]],[\"typed\",[0,2,3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 1, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[1, 4], [0, 2, 3]], [2, 3])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[1, 4], [0, 2, 3]], [2, 3])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0043","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91ebd5fc18abcc875da1d6bb93997023e4836e2aab686be275529882587eff30","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153043,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,4]],[\"typed\",[1,2,3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 1, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 4], [1, 2, 3]], [2, 3])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 4], [1, 2, 3]], [2, 3])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0044","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40a9dac27b877f6b65de48593a1bd4441d47e11a81a871c4e2191391c64d503c","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153044,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[4]],[\"typed\",[0,1,2,3]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 1, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[4], [0, 1, 2, 3]], [1, 4])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[4], [0, 1, 2, 3]], [1, 4])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0045","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf21bdbce13426ad8e82ea0c13a3c81d0a73ea268c85e685de2f923bf314b23f","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153045,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,2,3]],[\"typed\",[4]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 0, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 1, 2, 3], [4]], [4, 1])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 1, 2, 3], [4]], [4, 1])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0046","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a3d9dc3c2f4ff2bb81adcdaab92aebc427771ed87be60fb08b377758d6ca802","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153046,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,2,3]],[\"typed\",[0,4]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 0, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[1, 2, 3], [0, 4]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[1, 2, 3], [0, 4]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0047","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8514a4655753f15775369a91cb823d81e19de68998543a32151af473a54c120f","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153047,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,2,3]],[\"typed\",[1,4]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 1, 0, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 2, 3], [1, 4]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 2, 3], [1, 4]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0048","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c72d3eea33bc492345866461405c584a830f1d2d3f48fd95fd157626edf0236","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153048,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[2,3]],[\"typed\",[0,1,4]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 1, 0, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[2, 3], [0, 1, 4]], [2, 3])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[2, 3], [0, 1, 4]], [2, 3])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0049","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce4fd7b0d5e5077d1a43e0b986483f6c99f623fc9b6921ea8478039ecdcf7afe","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153049,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,3]],[\"typed\",[2,4]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0, 1, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[0, 1, 3], [2, 4]], [3, 2])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[0, 1, 3], [2, 4]], [3, 2])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0050","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e07a63f652011f9369fc3195a326378209183b523816d63e16cf8d1a0baeb123","family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153050,"semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,3]],[\"typed\",[0,2,4]]]"},"fields":{"title":"Two Typed Codomain Candidates and Their Preimages","stem":"Fin(5)={0,…,4} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[1, 0, 1, 0, 1] are indexed from 0. All entries must be typed, even unused ones. Ordered codomain candidates=[0, 1]. Give (candidate-type eligibility, preimage index lists or outside-codomain, sizes or outside-codomain). An outside value is not a legal empty preimage.","answer":{"kind":"expression","value":"([Yes, Yes], [[1, 3], [0, 2, 4]], [2, 3])","explanation":"Guard codomain typing before traversing every source output for equality; a legal unused codomain value has an empty preimage, while an outside candidate is ill-typed. The exact result, retaining the requested order, is ([Yes, Yes], [[1, 3], [0, 2, 4]], [2, 3])."},"skills":["Two Typed Codomain Candidates and Their Preimages"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0051","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c39c286004dca7c34447e2048eeff511a0b32f5846fe887c3a9b5458ec1cddf","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153051,"semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[0],1,[],[]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(1)={0,…,0} is the source and Fin(1)={0,…,0} the codomain; complete typed images=[0] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=0, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(0, [0], [0], [], [], 1)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (0, [0], [0], [], [], 1)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0052","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c898476dd32c21f24e45f2177486b8fa1058fd755a3f7ed59486d66f232ed6e","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153052,"semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[1,1],2,[0],[]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(2)={0,…,1} is the source and Fin(2)={0,…,1} the codomain; complete typed images=[0, 1] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=1, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(0, [1, 1], [1], [0], [], 2)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (0, [1, 1], [1], [0], [], 2)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0053","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36ba2bc8e58b83cce28ff255264a4068941390fe510eef09162b6307906ca4a3","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153053,"semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[2,0],3,[],[2]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(2)={0,…,1} is the source and Fin(3)={0,…,2} the codomain; complete typed images=[0, 0] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=2, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(0, [2, 0], [0, 2], [], [2], 3)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (0, [2, 0], [0, 2], [], [2], 3)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0054","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5f50f77e7ec2f57b71c7ca0e1734ffefc6007f6accc319ad1f3bc1042acd6b7d","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153054,"semantic_template":"qf-density15-typed-mapping-output-replacement/[1,[0,1],2,[],[]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(2)={0,…,1} is the source and Fin(2)={0,…,1} the codomain; complete typed images=[0, 1] are indexed from 0. All entries must be typed, even unused ones. Replace at=1 by new value=1, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(1, [0, 1], [0, 1], [], [], 2)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (1, [0, 1], [0, 1], [], [], 2)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0055","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eeff4b0f8e473d7f5ce61e4ecadb1f19b581a3208420b4e77f2e260f1c9b4d6d","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153055,"semantic_template":"qf-density15-typed-mapping-output-replacement/[4,[7,0,5],8,[4],[7]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[4, 0, 5] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=7, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(4, [7, 0, 5], [0, 5, 7], [4], [7], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (4, [7, 0, 5], [0, 5, 7], [4], [7], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0056","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c13c43b7639d14dbcf5a6737162fa4e6583ecd902e76d1a967a85fed38488247","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153056,"semantic_template":"qf-density15-typed-mapping-output-replacement/[5,[0,0,6],8,[5],[]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[5, 0, 6] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=0, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(5, [0, 0, 6], [0, 6], [5], [], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (5, [0, 0, 6], [0, 6], [5], [], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0057","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac811804dfeb32c9ef42cf4d10c28cfdee69bd2639cd3d0377de7e952fa131b5","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153057,"semantic_template":"qf-density15-typed-mapping-output-replacement/[6,[1,0,7],8,[6],[1]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[6, 0, 7] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=1, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(6, [1, 0, 7], [0, 1, 7], [6], [1], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (6, [1, 0, 7], [0, 1, 7], [6], [1], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0058","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b766e8d84b78f7490ea47a22d5372dbc381fd4fbe81f7718606d17febeb3c17a","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153058,"semantic_template":"qf-density15-typed-mapping-output-replacement/[7,[2,0,0],8,[7],[2]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[7, 0, 0] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=2, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(7, [2, 0, 0], [0, 2], [7], [2], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (7, [2, 0, 0], [0, 2], [7], [2], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0059","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad11e6ed89ae96709e64cb08cb7d4f0af9011aa4a016dbf51c8148d0b6fe58a7","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153059,"semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[3,1,1],8,[0],[3]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[0, 1, 1] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=3, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(0, [3, 1, 1], [1, 3], [0], [3], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (0, [3, 1, 1], [1, 3], [0], [3], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0060","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f4da2e4e6b76048ae1850f042cced0dbf808ab1a72cdf93c7c52f0931fcf88c","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153060,"semantic_template":"qf-density15-typed-mapping-output-replacement/[1,[4,1,2],8,[],[4]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[1, 1, 2] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=4, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(1, [4, 1, 2], [1, 2, 4], [], [4], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (1, [4, 1, 2], [1, 2, 4], [], [4], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0061","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec4d68580849f7fee63fbfcfde62b64770535d2f1e743613c7afd9694070a35b","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153061,"semantic_template":"qf-density15-typed-mapping-output-replacement/[2,[5,1,3],8,[2],[5]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[2, 1, 3] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=5, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(2, [5, 1, 3], [1, 3, 5], [2], [5], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (2, [5, 1, 3], [1, 3, 5], [2], [5], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0062","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"43e73559213cac3f8e1cfb5a698c1982c53ed169e43584253432d1fb975e0f9a","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153062,"semantic_template":"qf-density15-typed-mapping-output-replacement/[3,[6,1,4],8,[3],[6]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[3, 1, 4] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=6, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(3, [6, 1, 4], [1, 4, 6], [3], [6], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (3, [6, 1, 4], [1, 4, 6], [3], [6], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0063","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7d5be843ae2a6fec1811105abd1e49bcfe830ed5dfd88faf68a1cf1d9ac8a3b","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153063,"semantic_template":"qf-density15-typed-mapping-output-replacement/[4,[7,1,5],8,[4],[7]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[4, 1, 5] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=7, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(4, [7, 1, 5], [1, 5, 7], [4], [7], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (4, [7, 1, 5], [1, 5, 7], [4], [7], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0064","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2bada81caa0834aa4a1a27e974db747d1076a28c54c6caeb613b5e29d2ffd0e","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153064,"semantic_template":"qf-density15-typed-mapping-output-replacement/[5,[0,1,6],8,[5],[0]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[5, 1, 6] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=0, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(5, [0, 1, 6], [0, 1, 6], [5], [0], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (5, [0, 1, 6], [0, 1, 6], [5], [0], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0065","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f95ffe8f164bd87929bc956fe88214d4c4d70e953f6c55a1214de5daae19044a","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153065,"semantic_template":"qf-density15-typed-mapping-output-replacement/[6,[1,1,7],8,[6],[]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[6, 1, 7] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=1, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(6, [1, 1, 7], [1, 7], [6], [], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (6, [1, 1, 7], [1, 7], [6], [], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0066","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f193c5522d8af5ce4ab6def2d473973189158555faed51caa0aa576e0cefaa83","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153066,"semantic_template":"qf-density15-typed-mapping-output-replacement/[7,[2,1,0],8,[7],[2]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[7, 1, 0] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=2, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(7, [2, 1, 0], [0, 1, 2], [7], [2], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (7, [2, 1, 0], [0, 1, 2], [7], [2], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0067","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f77dbf53a6096185f044223144f66f0278fc07d337fca6ea861ace6dabdbcb4","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153067,"semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[3,2,1],8,[0],[3]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[0, 2, 1] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=3, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(0, [3, 2, 1], [1, 2, 3], [0], [3], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (0, [3, 2, 1], [1, 2, 3], [0], [3], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0068","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca08a013e2b8d73622db5a353ae7d33cc1dc3403a62a632771f7f91673d83162","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153068,"semantic_template":"qf-density15-typed-mapping-output-replacement/[1,[4,2,2],8,[1],[4]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[1, 2, 2] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=4, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(1, [4, 2, 2], [2, 4], [1], [4], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (1, [4, 2, 2], [2, 4], [1], [4], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0069","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa6643832b1ce8bf042b65c2e398ddfe978340d6b86c9bb7b815db7695b40133","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153069,"semantic_template":"qf-density15-typed-mapping-output-replacement/[2,[5,2,3],8,[],[5]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[2, 2, 3] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=5, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(2, [5, 2, 3], [2, 3, 5], [], [5], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (2, [5, 2, 3], [2, 3, 5], [], [5], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0070","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8f902ebd255be533708f444df7c071331fc9889c4c9177d90d1fd9e0f59aba8","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153070,"semantic_template":"qf-density15-typed-mapping-output-replacement/[3,[6,2,4],8,[3],[6]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[3, 2, 4] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=6, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(3, [6, 2, 4], [2, 4, 6], [3], [6], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (3, [6, 2, 4], [2, 4, 6], [3], [6], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0071","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f43d7bfa94a769262bacca2a7066b0e254a47edad9caf9a5a84da63e7bc905cb","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153071,"semantic_template":"qf-density15-typed-mapping-output-replacement/[4,[7,2,5],8,[4],[7]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[4, 2, 5] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=7, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(4, [7, 2, 5], [2, 5, 7], [4], [7], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (4, [7, 2, 5], [2, 5, 7], [4], [7], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0072","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"05059a7eface41859640fc10475714b89af55c501809979dfe21c4aacc0467fb","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153072,"semantic_template":"qf-density15-typed-mapping-output-replacement/[5,[0,2,6],8,[5],[0]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[5, 2, 6] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=0, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(5, [0, 2, 6], [0, 2, 6], [5], [0], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (5, [0, 2, 6], [0, 2, 6], [5], [0], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0073","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45ca83ab87d818c216d89ce6d58d522e7709218b66ab2c00ecea6934812efa35","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153073,"semantic_template":"qf-density15-typed-mapping-output-replacement/[6,[1,2,7],8,[6],[1]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[6, 2, 7] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=1, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(6, [1, 2, 7], [1, 2, 7], [6], [1], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (6, [1, 2, 7], [1, 2, 7], [6], [1], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0074","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fce41e1d843b062cbe19091e915daef549aaab8b6758c8108ae8abf50e2ce5ed","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153074,"semantic_template":"qf-density15-typed-mapping-output-replacement/[7,[2,2,0],8,[7],[]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[7, 2, 0] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=2, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(7, [2, 2, 0], [0, 2], [7], [], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (7, [2, 2, 0], [0, 2], [7], [], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0075","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1cccc9b4e4bd76fbf3a2cb350fe3789f6f847c21eabd38c09d27e9d1a8fd3c63","family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153075,"semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[3,3,1],8,[0],[]]"},"fields":{"title":"One Output Replacement and Range Additions/Removals","stem":"Fin(3)={0,…,2} is the source and Fin(8)={0,…,7} the codomain; complete typed images=[0, 3, 1] are indexed from 0. All entries must be typed, even unused ones. Replace at=0 by new value=3, after checking the whole original table. Give (old output, new table, new range, disappeared values, added values, m).","answer":{"kind":"expression","value":"(0, [3, 3, 1], [1, 3], [0], [], 8)","explanation":"Retain other table entries and compute both directional range differences; replacing by the same value does not manufacture an addition. The exact result, retaining the requested order, is (0, [3, 3, 1], [1, 3], [0], [], 8)."},"skills":["One Output Replacement and Range Additions/Removals"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0076","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fec359ae80afa93ec03ce7ae4ff83c26fc9934026899f51d318fdb08a72fbd44","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153076,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[0,0,[],[],[]]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(0)=∅, codomain=Fin(0)=∅; each input must have exactly one data row. Candidate raw rows=[]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([0, 0], [], [], [], [], Yes, [])","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([0, 0], [], [], [], [], Yes, [])."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0077","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"269e87d05fdfe949060efc80e5fb005c8ef3bab2a448d25a583bb0ef68f2b6da","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153077,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[1,1,[true],[1],[0]]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(1)={0,…,0}, codomain=Fin(1)={0,…,0}; each input must have exactly one data row. Candidate raw rows=[[0, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([1, 1], [Yes], [1], [], [], Yes, [0])","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([1, 1], [Yes], [1], [], [], Yes, [0])."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0078","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d73d5c94b5bcff43052bfcb97cc009ac762ae869f7de6293d4726b099034dec","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153078,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[1,1,[true,true],[2],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(1)={0,…,0}, codomain=Fin(1)={0,…,0}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [0, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([1, 1], [Yes, Yes], [2], [], [0], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([1, 1], [Yes, Yes], [2], [], [0], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0079","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a48b513779dc1ba65e4d525e38a4c25fa66b0693d03dd9afd111deb077118380","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153079,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[2,2,[true],[1,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(2)={0,…,1}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([2, 2], [Yes], [1, 0], [1], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([2, 2], [Yes], [1, 0], [1], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0080","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f7dc96db5159482543ac08cee3e258c535359d4a2a734e137fc8fec1eca625d8","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153080,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[2,2,[true,false],[1,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(2)={0,…,1}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [1, 2]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([2, 2], [Yes, No], [1, 1], [], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([2, 2], [Yes, No], [1, 1], [], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0081","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04231cb49ad952d31c2776571c2fd92d88a76389872387a193ccecd06c0869ff","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153081,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[2,2,[false,true,true],[1,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(2)={0,…,1}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[-1, 0], [0, 0], [1, 1]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([2, 2], [No, Yes, Yes], [1, 1], [], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([2, 2], [No, Yes, Yes], [1, 1], [], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0082","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"520cc602fe9aacc767d1373271088241ee88a1f61c1e461fdec1f40da09e0560","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153082,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[],[0,0,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [], [0, 0, 0], [0, 1, 2], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [], [0, 0, 0], [0, 1, 2], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0083","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"198ed89b2913e1f3283257cc7a0574116bc9a664565049f01bec47c627be60b8","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153083,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true],[1,0,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes], [1, 0, 0], [1, 2], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes], [1, 0, 0], [1, 2], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0084","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a705553ea6c8b1a95d8c3b2f3b4f9354d21c468da7ea7723bcfa94338ad6b709","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153084,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[2,0,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [0, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes], [2, 0, 0], [1, 2], [0], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes], [2, 0, 0], [1, 2], [0], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0085","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c5645abbf9b0852e31a196fdf66c4ad8deba6cd30c5d95a08bea3258e6a424f1","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153085,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true],[0,1,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[1, 1]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes], [0, 1, 0], [0, 2], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes], [0, 1, 0], [0, 2], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0086","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9f2de090d870b9cb45bf8397558ea5e62b3a5f0798dfa211f023e955e761439","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153086,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[1,1,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [1, 1]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes], [1, 1, 0], [2], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes], [1, 1, 0], [2], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0087","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0285b7b3a94a68aa88aa84b7350fdae29179f45dc729990ee2c54038751e75a6","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153087,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[2,1,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [0, 0], [1, 1]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes], [2, 1, 0], [2], [0], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes], [2, 1, 0], [2], [0], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0088","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ce9d50c4fca51801ee4a8f0e0525cb41154d0b3d4653a2270aad67da4524137","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153088,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,2,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[1, 1], [1, 1]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes], [0, 2, 0], [0, 2], [1], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes], [0, 2, 0], [0, 2], [1], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0089","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01bf11cde0b2c33a1caa5a8ba2b2e797222628a0b804725473d3a9bb70aa830d","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153089,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[1,2,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [1, 1], [1, 1]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes], [1, 2, 0], [2], [1], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes], [1, 2, 0], [2], [1], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0090","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b91c0813240c9cfe7c099e62ef5228a08847250bcf974b6aebdf5c1a260c5fb","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153090,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true],[2,2,0],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [0, 0], [1, 1], [1, 1]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes, Yes], [2, 2, 0], [2], [0, 1], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes, Yes], [2, 2, 0], [2], [0, 1], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0091","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"402d3d003cfa3ed8517fdd35ddc5bc0e734618bc1211a65318776a993ed0bf39","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153091,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true],[0,0,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes], [0, 0, 1], [0, 1], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes], [0, 0, 1], [0, 1], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0092","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"498a7bd7c905bfd061616a6f4712342859bd6ee86a6d979f51313c72b209f950","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153092,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[1,0,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes], [1, 0, 1], [1], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes], [1, 0, 1], [1], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0093","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"93b8da62523d240713aacc1050daa1cb109d9331e71223f1e43613346b91d3d6","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153093,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[2,0,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [0, 0], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes], [2, 0, 1], [1], [0], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes], [2, 0, 1], [1], [0], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0094","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf7e94a584433c58426ba4842075ce21deaf8a16d5dbd60a801a81770dd62858","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153094,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,1,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes], [0, 1, 1], [0], [], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes], [0, 1, 1], [0], [], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0095","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"031258a026ce6aded2b22aef95ea162ab0aca354ed200fdf31eff9144ed1b4c7","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153095,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[1,1,1],[0,1,0]]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes], [1, 1, 1], [], [], Yes, [0, 1, 0])","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes], [1, 1, 1], [], [], Yes, [0, 1, 0])."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0096","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"437e362f5c73996b1fc40bfc3f4004fc2c50de38f479e335ea20e3d044a4fe5c","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153096,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true],[2,1,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [0, 0], [1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes, Yes], [2, 1, 1], [], [0], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes, Yes], [2, 1, 1], [], [0], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0097","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1adb7fad736c29401ca5d75c0deeb5813aa888e2cc1f4cc999793ee2b3773b73","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153097,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[0,2,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[1, 1], [1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes], [0, 2, 1], [0], [1], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes], [0, 2, 1], [0], [1], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0098","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c2de47dd7a65c632a4cca17c7c6b5e60358b927dfb6433433ad459070db089d","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153098,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true],[1,2,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [1, 1], [1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes, Yes], [1, 2, 1], [], [1], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes, Yes], [1, 2, 1], [], [1], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0099","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc3ab8478bdab2880a75a07f345d6643be730d8b5ac76676d64cfc4a4f33def2","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153099,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true,true],[2,2,1],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[0, 0], [0, 0], [1, 1], [1, 1], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes, Yes, Yes, Yes], [2, 2, 1], [], [0, 1], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes, Yes, Yes, Yes], [2, 2, 1], [], [0, 1], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r03-domain-codomain-range-0100","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39ee03efe6370f3dfb4e9d558c04e47e86edfc5118bc21734a38d060f949bb7d","family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153100,"semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,0,2],\"not_total\"]"},"fields":{"title":"Candidate One-Row Protocol and Total-Table Eligibility","stem":"Source=Fin(3)={0,…,2}, codomain=Fin(2)={0,…,1}; each input must have exactly one data row. Candidate raw rows=[[2, 0], [2, 0]]. Give ([n,m], row-endpoint typing mask, raw occurrence counts for each legal input, missing inputs, repeated inputs, total-table eligibility, ordered images or not-total-table). Count by input before rejecting an outside output.","answer":{"kind":"expression","value":"([3, 2], [Yes, Yes], [0, 0, 2], [0, 1], [2], No, not-total-table)","explanation":"Audit every raw endpoint and each input’s row count separately; only a fully eligible representation becomes a total table. Equal-value duplicate rows violate this protocol but do not imply a multivalued mathematical function. The exact result, retaining the requested order, is ([3, 2], [Yes, Yes], [0, 0, 2], [0, 1], [2], No, not-total-table)."},"skills":["Candidate One-Row Protocol and Total-Table Eligibility"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}