{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0001","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0588b746526a23f4cbc42c78058471f3d12ba73a692c8592a0f6cf4a0b7f19f8","family_id":"qf-mod38-subseq-index-certificate","seed":202611077001,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":0,\"index_step\":1}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=0≥0 and positive integer index_step=1. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(0, 1, k(j)=0+1j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (0, 1, k(j)=0+1j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0002","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"248844a9355d8ea101d4ed382b465e174d00307225ed604ae6d6f9a514d315b5","family_id":"qf-mod38-subseq-index-certificate","seed":202611077002,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":1,\"index_step\":2}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=1≥0 and positive integer index_step=2. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(1, 2, k(j)=1+2j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (1, 2, k(j)=1+2j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0003","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1fdb97d7370ca68c787bf53d5e83c79eb877def74d3809184b60e2a079747ca","family_id":"qf-mod38-subseq-index-certificate","seed":202611077003,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":2,\"index_step\":3}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=2≥0 and positive integer index_step=3. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(2, 3, k(j)=2+3j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (2, 3, k(j)=2+3j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0004","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9851e936825b1bd260712d67ad788d99f1dd8eb6795ac215e8e6985f26280c23","family_id":"qf-mod38-subseq-index-certificate","seed":202611077004,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":3,\"index_step\":4}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=3≥0 and positive integer index_step=4. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(3, 4, k(j)=3+4j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (3, 4, k(j)=3+4j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0005","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8839d1a2f4e4719fe1b78dedf2438f1235f7d9d8726d33203c9cc226c454d593","family_id":"qf-mod38-subseq-index-certificate","seed":202611077005,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":4,\"index_step\":5}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=4≥0 and positive integer index_step=5. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(4, 5, k(j)=4+5j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (4, 5, k(j)=4+5j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0006","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8f9a1ddd8e5b1b82ef8e112485bba4c5c8cd151f554e3eb21445ce9d9f284929","family_id":"qf-mod38-subseq-index-certificate","seed":202611077006,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":5,\"index_step\":1}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=5≥0 and positive integer index_step=1. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(5, 1, k(j)=5+1j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (5, 1, k(j)=5+1j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0007","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecf25e0f5b4c755c9fd0243afc4ba1171a4cc69f2f2c243ee86aa0666923d06b","family_id":"qf-mod38-subseq-index-certificate","seed":202611077007,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":6,\"index_step\":2}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=6≥0 and positive integer index_step=2. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(6, 2, k(j)=6+2j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (6, 2, k(j)=6+2j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0008","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"554344c39815a1a51197ad338f8524d692f4179b8ba1dd39d079e809403b0421","family_id":"qf-mod38-subseq-index-certificate","seed":202611077008,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":7,\"index_step\":3}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=7≥0 and positive integer index_step=3. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(7, 3, k(j)=7+3j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (7, 3, k(j)=7+3j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0009","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c07d3082306a0fcbc34efaf86d0a11cc50ae2cba075a136e38083b86668b845","family_id":"qf-mod38-subseq-index-certificate","seed":202611077009,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":8,\"index_step\":4}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=8≥0 and positive integer index_step=4. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(8, 4, k(j)=8+4j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (8, 4, k(j)=8+4j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0010","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f38fa9d95fab84b0dc4c01751e3f4d038f6ed0c685f6a047f083e0f3cb12d672","family_id":"qf-mod38-subseq-index-certificate","seed":202611077010,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":9,\"index_step\":5}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=9≥0 and positive integer index_step=5. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(9, 5, k(j)=9+5j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (9, 5, k(j)=9+5j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0011","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf5b3a3577ba7a36be43471917771ca9b3aa9628e585991972e5a3e41d481b20","family_id":"qf-mod38-subseq-index-certificate","seed":202611077011,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":10,\"index_step\":1}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=10≥0 and positive integer index_step=1. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(10, 1, k(j)=10+1j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (10, 1, k(j)=10+1j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0012","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65ab20f23b9c0c2bd525535ec919a41e12a03281e01196f8e5f7b44c38d25c37","family_id":"qf-mod38-subseq-index-certificate","seed":202611077012,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":11,\"index_step\":2}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=11≥0 and positive integer index_step=2. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(11, 2, k(j)=11+2j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (11, 2, k(j)=11+2j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0013","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ad06d581079c314beff02e8e921e8ff69bfea07e77f49df24a6e7c660f4900f","family_id":"qf-mod38-subseq-index-certificate","seed":202611077013,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":12,\"index_step\":3}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=12≥0 and positive integer index_step=3. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(12, 3, k(j)=12+3j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (12, 3, k(j)=12+3j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0014","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12b0b62fdff32adde249ecdff65626bcd5df08690302558f431484a96beeba8e","family_id":"qf-mod38-subseq-index-certificate","seed":202611077014,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":13,\"index_step\":4}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=13≥0 and positive integer index_step=4. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(13, 4, k(j)=13+4j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (13, 4, k(j)=13+4j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0015","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"085376f7e26dd40c73832d6ab1c6ae6bad425123304412b0d8cc1539caa31a69","family_id":"qf-mod38-subseq-index-certificate","seed":202611077015,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":14,\"index_step\":5}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=14≥0 and positive integer index_step=5. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(14, 5, k(j)=14+5j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (14, 5, k(j)=14+5j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0016","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"35cee7fa27429a9b34ac5f50cd2913beb3ddb229f7e8982dc9e62d3a4316121e","family_id":"qf-mod38-subseq-index-certificate","seed":202611077016,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":15,\"index_step\":1}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=15≥0 and positive integer index_step=1. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(15, 1, k(j)=15+1j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (15, 1, k(j)=15+1j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0017","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c866c925a34ca0f8de25376015d1baf8ec3b9c3a7ea03d43af4ced203136ad11","family_id":"qf-mod38-subseq-index-certificate","seed":202611077017,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":16,\"index_step\":2}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=16≥0 and positive integer index_step=2. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(16, 2, k(j)=16+2j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (16, 2, k(j)=16+2j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0018","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd1c9360b6b32c6a61b40d398a48c3669343ab5ccdbce6b7035eee18619b00d1","family_id":"qf-mod38-subseq-index-certificate","seed":202611077018,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":17,\"index_step\":3}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=17≥0 and positive integer index_step=3. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(17, 3, k(j)=17+3j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (17, 3, k(j)=17+3j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0019","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c462d495e9f333dcaefb9f74ac355c71d8721ec0a8cf706bbccdbd6770878f8","family_id":"qf-mod38-subseq-index-certificate","seed":202611077019,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":18,\"index_step\":4}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=18≥0 and positive integer index_step=4. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(18, 4, k(j)=18+4j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (18, 4, k(j)=18+4j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0020","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e578b719ad85db5d377e4351996786ebe8dd548e61cd7d93c84c67254850fe32","family_id":"qf-mod38-subseq-index-certificate","seed":202611077020,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":19,\"index_step\":5}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=19≥0 and positive integer index_step=5. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(19, 5, k(j)=19+5j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (19, 5, k(j)=19+5j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0021","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ced889202714cb230e2ce551d41ac25b4827caa392398fcffa47ae7d9100af5c","family_id":"qf-mod38-subseq-index-certificate","seed":202611077021,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":20,\"index_step\":1}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=20≥0 and positive integer index_step=1. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(20, 1, k(j)=20+1j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (20, 1, k(j)=20+1j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0022","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9e91dcbfd625f56354e4a46d8d66b529d26af0a7165b3e90c185a2aad5ac5db","family_id":"qf-mod38-subseq-index-certificate","seed":202611077022,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":21,\"index_step\":2}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=21≥0 and positive integer index_step=2. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(21, 2, k(j)=21+2j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (21, 2, k(j)=21+2j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0023","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9af00d3906e1cf7bdf95cd44ff2e0c0b305c73f3a4d9de42f04a61d15ca695a","family_id":"qf-mod38-subseq-index-certificate","seed":202611077023,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":22,\"index_step\":3}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=22≥0 and positive integer index_step=3. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(22, 3, k(j)=22+3j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (22, 3, k(j)=22+3j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0024","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f176a170c88d1e7c486085aa370e9bec334b7872ef6f6bbb7dd41f751c2d71da","family_id":"qf-mod38-subseq-index-certificate","seed":202611077024,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":23,\"index_step\":4}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=23≥0 and positive integer index_step=4. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(23, 4, k(j)=23+4j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (23, 4, k(j)=23+4j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0025","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"647e5264cd66155302a634def1530d01c886575ca01e5748d227dde2cf2d6c98","family_id":"qf-mod38-subseq-index-certificate","seed":202611077025,"semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":24,\"index_step\":5}"},"fields":{"title":"A Positive Affine Index Step Gives Strict Increase for Every Natural Index","stem":"Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=24≥0 and positive integer index_step=5. Give (index_start, index_step, index_formula, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(24, 5, k(j)=24+5j, Yes, strictly_increasing_for_all_natural_j)","explanation":"The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (24, 5, k(j)=24+5j, Yes, strictly_increasing_for_all_natural_j)."},"skills":["A Positive Affine Index Step Gives Strict Increase for Every Natural Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0026","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5e8503a794ca362d6c9e0ac5b2c1f9dc7d5b794cee887c163dc339216336b27","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077026,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":1,\"j\":2,\"source_start\":1,\"source_step\":1}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=1+(1)n for n≥0 and index map k(j)=0+1j, with nonnegative start and positive index step. Evaluate j=2. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(2, 2, 3, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (2, 2, 3, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0027","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"873323b442bd8537125ad2e47a81fdeefcb333fa529ab28716423a8fff9166ba","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077027,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":2,\"j\":3,\"source_start\":2,\"source_step\":2}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=2+(2)n for n≥0 and index map k(j)=1+2j, with nonnegative start and positive index step. Evaluate j=3. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(3, 7, 16, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (3, 7, 16, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0028","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9143da740a71e88ceb4e19b9ae137900247f79fbe2cf0c948ccf10fb9a24489","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077028,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":3,\"j\":4,\"source_start\":3,\"source_step\":3}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=3+(3)n for n≥0 and index map k(j)=2+3j, with nonnegative start and positive index step. Evaluate j=4. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(4, 14, 45, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (4, 14, 45, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0029","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c28d132a5bf173107de3abc4037e9e20048269611ff54d28b2152fbe05794b8a","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077029,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":4,\"j\":5,\"source_start\":4,\"source_step\":4}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=4+(4)n for n≥0 and index map k(j)=3+4j, with nonnegative start and positive index step. Evaluate j=5. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(5, 23, 96, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (5, 23, 96, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0030","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7cc0e9f390187d1dcc2ebcb5bc4a5f84d2d137de49191fbd296c34f1d5eac5b","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077030,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":5,\"j\":6,\"source_start\":5,\"source_step\":5}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=5+(5)n for n≥0 and index map k(j)=0+5j, with nonnegative start and positive index step. Evaluate j=6. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(6, 30, 155, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (6, 30, 155, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0031","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bba4e2cee0e85e628359e1678ea877c1c9114df6315926842fb673e6082345d4","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077031,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":1,\"j\":7,\"source_start\":6,\"source_step\":6}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=6+(6)n for n≥0 and index map k(j)=1+1j, with nonnegative start and positive index step. Evaluate j=7. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(7, 8, 54, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (7, 8, 54, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0032","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48a34795723c6e0c1b353f6e3ed8c3491f74f4fcabfb431c484e4896bfccc774","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077032,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":2,\"j\":8,\"source_start\":7,\"source_step\":7}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=7+(7)n for n≥0 and index map k(j)=2+2j, with nonnegative start and positive index step. Evaluate j=8. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(8, 18, 133, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (8, 18, 133, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0033","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"883e4972248be2916e5da8260fb2f2addf6cb94a22652af5a79b6922943d4123","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077033,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":3,\"j\":9,\"source_start\":8,\"source_step\":1}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=8+(1)n for n≥0 and index map k(j)=3+3j, with nonnegative start and positive index step. Evaluate j=9. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(9, 30, 38, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (9, 30, 38, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0034","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f84d2b0447240cd8687115e9a10d33c4eed24fb6cee71d5377a12c7bab50c9d","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077034,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":4,\"j\":10,\"source_start\":9,\"source_step\":2}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=9+(2)n for n≥0 and index map k(j)=0+4j, with nonnegative start and positive index step. Evaluate j=10. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(10, 40, 89, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (10, 40, 89, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0035","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd6d3e4f8383a16779bc11090bc1a610e9cf7ee7e7955e04b924777a422e2af6","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077035,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":5,\"j\":11,\"source_start\":10,\"source_step\":3}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=10+(3)n for n≥0 and index map k(j)=1+5j, with nonnegative start and positive index step. Evaluate j=11. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(11, 56, 178, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (11, 56, 178, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0036","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"475ad8866edb799d01982f552e1ed1a27034701f833bd372503b4165dba9600f","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077036,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":1,\"j\":12,\"source_start\":11,\"source_step\":4}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=11+(4)n for n≥0 and index map k(j)=2+1j, with nonnegative start and positive index step. Evaluate j=12. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(12, 14, 67, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (12, 14, 67, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0037","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9047a75e00ada9e81d1a674b9a02245938f46dab6697e142c8332158afc4b4ab","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077037,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":2,\"j\":13,\"source_start\":12,\"source_step\":5}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=12+(5)n for n≥0 and index map k(j)=3+2j, with nonnegative start and positive index step. Evaluate j=13. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(13, 29, 157, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (13, 29, 157, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0038","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a580b3e6d9c475ade97ca75f72a81c8331575ca8e9641b8a492ad1dbb5e679e","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077038,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":3,\"j\":14,\"source_start\":13,\"source_step\":6}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=13+(6)n for n≥0 and index map k(j)=0+3j, with nonnegative start and positive index step. Evaluate j=14. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(14, 42, 265, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (14, 42, 265, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0039","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00a5931f3cd5f55fb1e9a9c6662db65520aa1abdfe21c8ee1adfa4d54d3aad4c","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077039,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":4,\"j\":15,\"source_start\":14,\"source_step\":7}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=14+(7)n for n≥0 and index map k(j)=1+4j, with nonnegative start and positive index step. Evaluate j=15. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(15, 61, 441, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (15, 61, 441, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0040","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd349fcd907c366bbebe090187d15def75e009a7de7111cfa3351f62194ff61f","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077040,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":5,\"j\":16,\"source_start\":15,\"source_step\":1}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=15+(1)n for n≥0 and index map k(j)=2+5j, with nonnegative start and positive index step. Evaluate j=16. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(16, 82, 97, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (16, 82, 97, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0041","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d0f647d2744f272cd14050b4e49d4e08f9299b084cca20a2d696b4e6409d31e4","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077041,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":1,\"j\":17,\"source_start\":16,\"source_step\":2}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=16+(2)n for n≥0 and index map k(j)=3+1j, with nonnegative start and positive index step. Evaluate j=17. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(17, 20, 56, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (17, 20, 56, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0042","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0380d622f61a5ba1d382d46d2f2ac82e814738867da95a529afdf814a79c7086","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077042,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":2,\"j\":18,\"source_start\":17,\"source_step\":3}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=17+(3)n for n≥0 and index map k(j)=0+2j, with nonnegative start and positive index step. Evaluate j=18. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(18, 36, 125, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (18, 36, 125, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0043","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"59fd5d1b21b6330fa525b1c18a4ae8f69beed752bc016f9e2e7eab65d3fa8f39","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077043,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":3,\"j\":19,\"source_start\":18,\"source_step\":4}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=18+(4)n for n≥0 and index map k(j)=1+3j, with nonnegative start and positive index step. Evaluate j=19. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(19, 58, 250, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (19, 58, 250, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0044","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c1288c30c07842663b143183aabaab5a960167e217f654eb42c6a6203dacb49","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077044,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":4,\"j\":20,\"source_start\":19,\"source_step\":5}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=19+(5)n for n≥0 and index map k(j)=2+4j, with nonnegative start and positive index step. Evaluate j=20. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(20, 82, 429, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (20, 82, 429, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0045","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f50eb511de8c9f1db17ecea377524a5973817e8f1f935c3cf7d1b43e9864f1a","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077045,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":5,\"j\":21,\"source_start\":20,\"source_step\":6}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=20+(6)n for n≥0 and index map k(j)=3+5j, with nonnegative start and positive index step. Evaluate j=21. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(21, 108, 668, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (21, 108, 668, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0046","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25b7918c2a7f5659f3c74e0a9fa5ee189e41fa105654b0fe73e13e87747b3099","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077046,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":1,\"j\":22,\"source_start\":21,\"source_step\":7}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=21+(7)n for n≥0 and index map k(j)=0+1j, with nonnegative start and positive index step. Evaluate j=22. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(22, 22, 175, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (22, 22, 175, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0047","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a206c191a40424738517dd6c06b605c101bc3407fcbab3a39973564345828700","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077047,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":2,\"j\":23,\"source_start\":22,\"source_step\":1}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=22+(1)n for n≥0 and index map k(j)=1+2j, with nonnegative start and positive index step. Evaluate j=23. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(23, 47, 69, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (23, 47, 69, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0048","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b374447be7dc9f28a0bcb6a9e808f9ab86714b63f834afb0817140038278880f","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077048,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":3,\"j\":24,\"source_start\":23,\"source_step\":2}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=23+(2)n for n≥0 and index map k(j)=2+3j, with nonnegative start and positive index step. Evaluate j=24. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(24, 74, 171, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (24, 74, 171, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0049","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18e25e1132201c7833e1aa274ea1babb8fb39350b6df540812d5715501840011","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077049,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":4,\"j\":25,\"source_start\":24,\"source_step\":3}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=24+(3)n for n≥0 and index map k(j)=3+4j, with nonnegative start and positive index step. Evaluate j=25. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(25, 103, 333, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (25, 103, 333, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0050","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d96d03d370a3d9621c1bd041902938d58f5e65ed24bf6ff573c72a589e108e72","family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077050,"semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":5,\"j\":26,\"source_start\":25,\"source_step\":4}"},"fields":{"title":"A Subsequence Term Uses the Source at Its Increasing Selected Index","stem":"Use the entire arithmetic source a_n=25+(4)n for n≥0 and index map k(j)=0+5j, with nonnegative start and positive index step. Evaluate j=26. Give (j, source_index, subsequence_term, certificate).","answer":{"kind":"expression","value":"(26, 130, 545, a_of_k_j_preserves_original_order)","explanation":"Compute the selected source index and then a at that index, retaining original sequence order even when the source values decrease. The adapter rejects unsafe Number-range integer products rather than projecting rounded values. The exact result, retaining the requested order, is (26, 130, 545, a_of_k_j_preserves_original_order)."},"skills":["A Subsequence Term Uses the Source at Its Increasing Selected Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0051","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1066c4597784e65c7d104ad3c25da8c2cb451f1ff5d988d34f127537629f6948","family_id":"qf-mod38-subseq-composed-index","seed":202611077051,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":1,\"j\":1,\"outer_start\":0,\"outer_step\":1}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+1i and inner index l(j)=0+1j, with nonnegative starts and positive steps. Evaluate j=1. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(1, 1, 1, 1, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (1, 1, 1, 1, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0052","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38ccc0f4d55ade18a79f26c9232ba880177e83f21fdd28c4e4fd64bea12dcd24","family_id":"qf-mod38-subseq-composed-index","seed":202611077052,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":2,\"j\":2,\"outer_start\":1,\"outer_step\":2}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+2i and inner index l(j)=1+2j, with nonnegative starts and positive steps. Evaluate j=2. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(2, 5, 11, 4, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (2, 5, 11, 4, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0053","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fee46af53732445667c38226a61170385e4cc4a14e03859349a2d741e156c623","family_id":"qf-mod38-subseq-composed-index","seed":202611077053,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":3,\"j\":3,\"outer_start\":2,\"outer_step\":3}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+3i and inner index l(j)=2+3j, with nonnegative starts and positive steps. Evaluate j=3. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(3, 11, 35, 9, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (3, 11, 35, 9, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0054","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"97070041879c0529cfba340abb60e8c02beadef47832d2c4eae6ffc80d70010c","family_id":"qf-mod38-subseq-composed-index","seed":202611077054,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":4,\"j\":4,\"outer_start\":0,\"outer_step\":4}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+4i and inner index l(j)=3+4j, with nonnegative starts and positive steps. Evaluate j=4. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(4, 19, 76, 16, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (4, 19, 76, 16, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0055","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e18444d8ba03f1f88ea55a5edfb64aa1b7849ff219934f495f602909f91c1e7d","family_id":"qf-mod38-subseq-composed-index","seed":202611077055,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":5,\"j\":5,\"outer_start\":1,\"outer_step\":5}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+5i and inner index l(j)=0+5j, with nonnegative starts and positive steps. Evaluate j=5. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(5, 25, 126, 25, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (5, 25, 126, 25, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0056","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fdfd1661d10d1d7514ea0c710eb838f016871099898fdbd7c9ce01e536f2aea8","family_id":"qf-mod38-subseq-composed-index","seed":202611077056,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":6,\"j\":6,\"outer_start\":2,\"outer_step\":1}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+1i and inner index l(j)=1+6j, with nonnegative starts and positive steps. Evaluate j=6. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(6, 37, 39, 6, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (6, 37, 39, 6, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0057","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"69012b74ca715c54434b854be74291adce1c0fa34e28cb65794475339cc91c97","family_id":"qf-mod38-subseq-composed-index","seed":202611077057,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":1,\"j\":7,\"outer_start\":0,\"outer_step\":2}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+2i and inner index l(j)=2+1j, with nonnegative starts and positive steps. Evaluate j=7. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(7, 9, 18, 2, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (7, 9, 18, 2, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0058","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ce6208892067e4f8ee385301aaadf3abce11a429ecfbbc6552d73b1644a235d","family_id":"qf-mod38-subseq-composed-index","seed":202611077058,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":2,\"j\":8,\"outer_start\":1,\"outer_step\":3}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+3i and inner index l(j)=3+2j, with nonnegative starts and positive steps. Evaluate j=8. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(8, 19, 58, 6, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (8, 19, 58, 6, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0059","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61490b7bc22347fa142a176f110682390a3e04bcc4aa02268c34114e2398641a","family_id":"qf-mod38-subseq-composed-index","seed":202611077059,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":3,\"j\":9,\"outer_start\":2,\"outer_step\":4}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+4i and inner index l(j)=0+3j, with nonnegative starts and positive steps. Evaluate j=9. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(9, 27, 110, 12, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (9, 27, 110, 12, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0060","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b0ccf2cd66be3d1d5f03e9f9f40573e2b245731c7a65680d0053ca4fd95d83b","family_id":"qf-mod38-subseq-composed-index","seed":202611077060,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":4,\"j\":10,\"outer_start\":0,\"outer_step\":5}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+5i and inner index l(j)=1+4j, with nonnegative starts and positive steps. Evaluate j=10. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(10, 41, 205, 20, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (10, 41, 205, 20, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0061","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4d59f67a3f37e80faa6b3e334262dadd0f19c66f44a628b80c1e542ae9a455c","family_id":"qf-mod38-subseq-composed-index","seed":202611077061,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":5,\"j\":11,\"outer_start\":1,\"outer_step\":1}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+1i and inner index l(j)=2+5j, with nonnegative starts and positive steps. Evaluate j=11. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(11, 57, 58, 5, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (11, 57, 58, 5, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0062","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"578f2a1ca58f6ac198f975e08014ae914833d375b0d41e673aac19aa5eb0b8c0","family_id":"qf-mod38-subseq-composed-index","seed":202611077062,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":6,\"j\":12,\"outer_start\":2,\"outer_step\":2}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+2i and inner index l(j)=3+6j, with nonnegative starts and positive steps. Evaluate j=12. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(12, 75, 152, 12, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (12, 75, 152, 12, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0063","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffbaa990de7c51cf447facde8660c9d65b5c8554273a049b86d3cc146b3192ba","family_id":"qf-mod38-subseq-composed-index","seed":202611077063,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":1,\"j\":13,\"outer_start\":0,\"outer_step\":3}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+3i and inner index l(j)=0+1j, with nonnegative starts and positive steps. Evaluate j=13. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(13, 13, 39, 3, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (13, 13, 39, 3, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0064","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b3ffb1f0e7fa6e1a39ca1ac546b6c8326d532ae953d4d42d02ddafd7b5927370","family_id":"qf-mod38-subseq-composed-index","seed":202611077064,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":2,\"j\":14,\"outer_start\":1,\"outer_step\":4}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+4i and inner index l(j)=1+2j, with nonnegative starts and positive steps. Evaluate j=14. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(14, 29, 117, 8, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (14, 29, 117, 8, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0065","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8d9d1a9c02da541802bb61f2befdd51028f56d8bd603d98c4a8838eb16140ee3","family_id":"qf-mod38-subseq-composed-index","seed":202611077065,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":3,\"j\":15,\"outer_start\":2,\"outer_step\":5}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+5i and inner index l(j)=2+3j, with nonnegative starts and positive steps. Evaluate j=15. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(15, 47, 237, 15, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (15, 47, 237, 15, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0066","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"907f65f2945c4a37abbf1097b69c6283a8d9888a943eb820698a67f5b1427617","family_id":"qf-mod38-subseq-composed-index","seed":202611077066,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":4,\"j\":16,\"outer_start\":0,\"outer_step\":1}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+1i and inner index l(j)=3+4j, with nonnegative starts and positive steps. Evaluate j=16. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(16, 67, 67, 4, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (16, 67, 67, 4, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0067","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68f4c34f184ab3494812e645e2af90c25b552db6ad787b21f3bf0b10edbccffb","family_id":"qf-mod38-subseq-composed-index","seed":202611077067,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":5,\"j\":17,\"outer_start\":1,\"outer_step\":2}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+2i and inner index l(j)=0+5j, with nonnegative starts and positive steps. Evaluate j=17. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(17, 85, 171, 10, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (17, 85, 171, 10, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0068","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5224e9ad1b693c2b37b50d21f35b803bd12b890d16d8d1092bcbfac118b3afa","family_id":"qf-mod38-subseq-composed-index","seed":202611077068,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":6,\"j\":18,\"outer_start\":2,\"outer_step\":3}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+3i and inner index l(j)=1+6j, with nonnegative starts and positive steps. Evaluate j=18. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(18, 109, 329, 18, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (18, 109, 329, 18, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0069","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"769607febe4b8e188eb67a6808561e8a6fc45bad3e20b7ea45c4f39959abe00a","family_id":"qf-mod38-subseq-composed-index","seed":202611077069,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":1,\"j\":19,\"outer_start\":0,\"outer_step\":4}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+4i and inner index l(j)=2+1j, with nonnegative starts and positive steps. Evaluate j=19. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(19, 21, 84, 4, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (19, 21, 84, 4, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0070","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"448301b5af448bcae515fa942ce6cd5dd5921ca7c3a262e7a94f5bd1a4c015af","family_id":"qf-mod38-subseq-composed-index","seed":202611077070,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":2,\"j\":20,\"outer_start\":1,\"outer_step\":5}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+5i and inner index l(j)=3+2j, with nonnegative starts and positive steps. Evaluate j=20. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(20, 43, 216, 10, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (20, 43, 216, 10, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0071","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66957ece2649eedb5be72dfd79a0aa80aff8a9f767c2060674534f1ae624e4d1","family_id":"qf-mod38-subseq-composed-index","seed":202611077071,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":3,\"j\":21,\"outer_start\":2,\"outer_step\":1}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+1i and inner index l(j)=0+3j, with nonnegative starts and positive steps. Evaluate j=21. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(21, 63, 65, 3, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (21, 63, 65, 3, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0072","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f3b4f9a83343a5d2b6ada0791237745a2f3a6645f438bb1be43062ea2518c0e","family_id":"qf-mod38-subseq-composed-index","seed":202611077072,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":4,\"j\":22,\"outer_start\":0,\"outer_step\":2}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+2i and inner index l(j)=1+4j, with nonnegative starts and positive steps. Evaluate j=22. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(22, 89, 178, 8, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (22, 89, 178, 8, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0073","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37939cceff3d6638b7ade750944a8a50e845d647df6147015456355198de69a6","family_id":"qf-mod38-subseq-composed-index","seed":202611077073,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":5,\"j\":23,\"outer_start\":1,\"outer_step\":3}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=1+3i and inner index l(j)=2+5j, with nonnegative starts and positive steps. Evaluate j=23. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(23, 117, 352, 15, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (23, 117, 352, 15, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0074","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f7ba2406922d24153176eb81f5fb653a249f638a2bbd0f537a805a2e9653bc7","family_id":"qf-mod38-subseq-composed-index","seed":202611077074,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":6,\"j\":24,\"outer_start\":2,\"outer_step\":4}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=2+4i and inner index l(j)=3+6j, with nonnegative starts and positive steps. Evaluate j=24. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(24, 147, 590, 24, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (24, 147, 590, 24, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0075","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e1683698e8cf08f0b96e1b321d1ca110a4134d8e8c341afae788372a2e4fc89","family_id":"qf-mod38-subseq-composed-index","seed":202611077075,"semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":1,\"j\":25,\"outer_start\":0,\"outer_step\":5}"},"fields":{"title":"Compose the Inner Index into the Outer Index in That Order","stem":"Use outer index k(i)=0+5i and inner index l(j)=0+1j, with nonnegative starts and positive steps. Evaluate j=25. Give (j, inner_index, source_index, composed_step, strictly_increasing, certificate).","answer":{"kind":"expression","value":"(25, 25, 125, 5, Yes, composition_remains_strictly_increasing)","explanation":"Compute l(j), then k(l(j)); the composed positive step is outer_step*inner_step. This order is not an arbitrary rearrangement of the source. Unsafe exact-integer results are rejected before English projection. The exact result, retaining the requested order, is (25, 25, 125, 5, Yes, composition_remains_strictly_increasing)."},"skills":["Compose the Inner Index into the Outer Index in That Order"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0076","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1807211ac172c8ef1dc7279688d43ab6d1b6c316c88c4252958f039c4ebaff16","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077076,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[0,1,2,3]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[0, 1, 2, 3]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([0, 1, 2, 3], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([0, 1, 2, 3], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0077","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca7ef765f1555bcbcf8ddedafaafdb4c24217564976a924388726cef4e90c0f2","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077077,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[1,3,5,7,9]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[1, 3, 5, 7, 9]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([1, 3, 5, 7, 9], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0078","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e610c089cf6a25344f64d087db97b433abb71b76c9662c3d7c0bea6a8d3da0b","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077078,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[2,5,8,11,14,17]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[2, 5, 8, 11, 14, 17]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([2, 5, 8, 11, 14, 17], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([2, 5, 8, 11, 14, 17], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0079","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1e5776076d4cc09050e307625d2d4d24d8971af4560ba33be76045cbabadcbd","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077079,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[3,7,11,15]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[3, 7, 11, 15]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([3, 7, 11, 15], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([3, 7, 11, 15], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0080","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"22e05af14ea2b394ec4d0da3e53e98c736957e546e0b923a4592a372ab13ef40","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077080,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[4,9,14,19,24]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[4, 9, 14, 19, 24]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([4, 9, 14, 19, 24], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([4, 9, 14, 19, 24], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0081","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"14e253d65562fd0e39d3ef81964b173bdc2e0751cbe2aea1fa268ca9b9e247e7","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077081,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[5,6,7,8,9,10]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[5, 6, 7, 8, 9, 10]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([5, 6, 7, 8, 9, 10], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([5, 6, 7, 8, 9, 10], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0082","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c054cf14cc0fdf78d0284804989100f6660fdaf242d6f92b1d8c0da35dcbe0f","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077082,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[6,8,10,12]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[6, 8, 10, 12]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([6, 8, 10, 12], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([6, 8, 10, 12], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0083","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b144526d937bbecc2906b5363451935986be372d14e0edf03cd2740c82efa34","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077083,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[7,10,13,16,19]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[7, 10, 13, 16, 19]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([7, 10, 13, 16, 19], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([7, 10, 13, 16, 19], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0084","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"999a4064434d75d6c7ade97cc6e790e3d935cf06a9a257c283020ac6abff2f50","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077084,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[8,12,16,20,24,28]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[8, 12, 16, 20, 24, 28]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([8, 12, 16, 20, 24, 28], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([8, 12, 16, 20, 24, 28], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0085","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b79570144fa3a557340479cc5b576c1be4fd24a721054e63a0f22a02c817a113","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077085,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[9,14,19,24]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[9, 14, 19, 24]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([9, 14, 19, 24], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([9, 14, 19, 24], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0086","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42c879ed4ad3ad68d31cfe3489f81a52772e40955799718104badbf60dde39f2","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077086,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[10,11,12,13,14]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[10, 11, 12, 13, 14]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([10, 11, 12, 13, 14], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([10, 11, 12, 13, 14], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0087","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0241b8d42457a92d53366c6fd85c6826cbe905c5c7d5618cfdb2167962c1e604","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077087,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[11,13,15,17,19,21]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[11, 13, 15, 17, 19, 21]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([11, 13, 15, 17, 19, 21], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([11, 13, 15, 17, 19, 21], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0088","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53724942ecdcb3787f73534d0845784d17b71793f79e6bd15bfb5ac1e06bf23c","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077088,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[12,15,18,21]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[12, 15, 18, 21]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([12, 15, 18, 21], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([12, 15, 18, 21], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0089","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1caea715a7d911f22ee79670a75683b4496a57761f450eddbafc40e491a59082","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077089,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[13,17,21,25,29]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[13, 17, 21, 25, 29]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([13, 17, 21, 25, 29], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([13, 17, 21, 25, 29], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0090","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"05a9035ef4926fb70a78bd0aa2ffbf95302f62aa133d6828af57028d93159c65","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077090,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[14,19,24,29,34,39]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[14, 19, 24, 29, 34, 39]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([14, 19, 24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([14, 19, 24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0091","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09064acd115ecdf9a0393202dc1bcfbcfa8ad6e3ad8b48ff371eb3a95799f018","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077091,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[15,16,17,18]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[15, 16, 17, 18]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([15, 16, 17, 18], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([15, 16, 17, 18], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0092","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b7b57b9ad46dadc829e822e681ea7329987b7ad23fada3fd6c1b53088abe482","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077092,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[16,18,20,22,24]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[16, 18, 20, 22, 24]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([16, 18, 20, 22, 24], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([16, 18, 20, 22, 24], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0093","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b05352f4eb514137a2721b3705eeef876298b159e472b233a55a77610f52206f","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077093,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[17,20,23,26,29,32]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[17, 20, 23, 26, 29, 32]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([17, 20, 23, 26, 29, 32], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([17, 20, 23, 26, 29, 32], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0094","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a71664d9da4df8a7b6e0c05a7794d10091ca53b55ef7a78a2ce9539ce6d21dee","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077094,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[18,22,26,30]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[18, 22, 26, 30]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([18, 22, 26, 30], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([18, 22, 26, 30], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0095","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab7dbbcc7e51b31972c89a556876295443718fc62ac0c66ac665ca4276964e96","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077095,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[19,24,29,34,39]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[19, 24, 29, 34, 39]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([19, 24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([19, 24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0096","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6cc2037392b03fcd70db9592b0c2bf3497c3efc3d94ccca174cc3333efa96db","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077096,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[20,21,22,23,24,25]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[20, 21, 22, 23, 24, 25]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([20, 21, 22, 23, 24, 25], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([20, 21, 22, 23, 24, 25], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0097","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fdbc1e8ab4b55fe88e6a594a6e18b0fbcdc6dd97f534038733a1241af897cf25","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077097,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[21,23,25,27]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[21, 23, 25, 27]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([21, 23, 25, 27], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([21, 23, 25, 27], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0098","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5118e7a1755aa1a7e0870375ddead3e6c51779170d87f2ae344ee273d2c63d81","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077098,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[22,25,28,31,34]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[22, 25, 28, 31, 34]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([22, 25, 28, 31, 34], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([22, 25, 28, 31, 34], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0099","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41aca15042306391c1436c0592c92416bf7c86db8399d533714b828946c5e7be","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077099,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[23,27,31,35,39,43]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[23, 27, 31, 35, 39, 43]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([23, 27, 31, 35, 39, 43], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([23, 27, 31, 35, 39, 43], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261107-r07-subsequence-0100","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c49b55a483039d73048bbfaee35173281afb46dec0eacaa3dd47b7eee821c57","family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077100,"semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[24,29,34,39]}"},"fields":{"title":"A Finite Increasing List Is Not an Already-Supplied Infinite Certificate","stem":"Supplied finite natural-index list=[24, 29, 34, 39]. Give (indices, finite_prefix_increasing, infinite_certificate_supplied, boundary).","answer":{"kind":"expression","value":"([24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation":"Check only strict increase of this finite list, then No for an infinite index certificate supplied by that data alone. This does not deny that an increasing finite prefix can be extended; it keeps a finite observation distinct from a stated all-j map. The exact result, retaining the requested order, is ([24, 29, 34, 39], Yes, No, finite_increasing_prefix_not_infinite_subsequence_certificate)."},"skills":["A Finite Increasing List Is Not an Already-Supplied Infinite Certificate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}