{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261014-advance-20261029-r05-finite-filtration-0001","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1dead1c5975b7ac460e7b090a6ee06b26cd76180da90d281cc7097c61ac77c5c","family_id":"qf-mod29-filtration-qualification","seed":202610295001,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,0,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], No)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], No)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0002","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40d3f6a399d7dc7d39171c4ea14635ba02c674b694c44e8ace0fb76cce962f08","family_id":"qf-mod29-filtration-qualification","seed":202610295002,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0003","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f463f449bb61908efb23fea2e7bc4e37bd3a7574d2af04126c1161bc89761f49","family_id":"qf-mod29-filtration-qualification","seed":202610295003,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0004","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"73f29b409692bda758c47046ddd14acfb809a2be965538d5d47b168cc713a9e8","family_id":"qf-mod29-filtration-qualification","seed":202610295004,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0005","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"900f63bf2a1795735d5f7a60008a3e49423cf3d22e8d9277975d9accb4ff2001","family_id":"qf-mod29-filtration-qualification","seed":202610295005,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0006","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fbaaaa8504680a1af10550e2dbfb25829a4f96266c32c9906a3ff877dde052e4","family_id":"qf-mod29-filtration-qualification","seed":202610295006,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,1,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 1, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 2, 3]], No)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [[2, 0, 3], [2, 2, 3]], No)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0007","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a9534dd54e4dbf5532762909370f9db3dbf3f2921604c1b49ea7b8de53af3b9c","family_id":"qf-mod29-filtration-qualification","seed":202610295007,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0008","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36958c14bf3e9f1c1e6cd576ea493f5233b01218b397c62c5f81dfa17213a99a","family_id":"qf-mod29-filtration-qualification","seed":202610295008,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0009","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1651b9107e9f0456128d917956450493f78047f05166aa4a88e0575cec1e4261","family_id":"qf-mod29-filtration-qualification","seed":202610295009,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0010","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"adbb0711e6f28ab3d3fe9d6c6c1a7a7fcc4ae655cee911a29f1578157022051c","family_id":"qf-mod29-filtration-qualification","seed":202610295010,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0011","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c704e142e5760f99efa9c8fda8473794035cf326b6d489e9be6dd277f44c330","family_id":"qf-mod29-filtration-qualification","seed":202610295011,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,0,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 2, 3]], No)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [[2, 0, 3], [2, 2, 3]], No)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0012","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"160961dabc3d232e6a440d31650bfa331c1913fe8647e01319cbe7f2e59be6f9","family_id":"qf-mod29-filtration-qualification","seed":202610295012,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0013","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4f10f00f29755328f09f4bfcd550c24fcf6d2b8b86accc1b3c1d951e5d5c46e","family_id":"qf-mod29-filtration-qualification","seed":202610295013,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0014","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5473381a7f6dcc6010db366b082c21a1cd6d9b17f102a6bef3e834fb0f822a7","family_id":"qf-mod29-filtration-qualification","seed":202610295014,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0015","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"585662d8d92e5c03140ca0def85706049c19bb238964842fd595ebb3429f8704","family_id":"qf-mod29-filtration-qualification","seed":202610295015,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0016","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36739bd85eb1347c3614ae1a05d95c0dc2306094d0fa9e068f24bf1ae1a4f3fa","family_id":"qf-mod29-filtration-qualification","seed":202610295016,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,1,10,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 1, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], No)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], No)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0017","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e7e5137ee94e66118c4892ec0ec66c65fb6aeb089d2d728311dc96736ea8072","family_id":"qf-mod29-filtration-qualification","seed":202610295017,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0018","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ee8d2b4b1fca1d1405c7c350ae8f9dd4f05a95d78fcea2ed14dac375399b425","family_id":"qf-mod29-filtration-qualification","seed":202610295018,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0019","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffcf56c5f9341edeebf275f9ac46518dbb373e5f29cfd17a4029a5f8f4a06151","family_id":"qf-mod29-filtration-qualification","seed":202610295019,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0020","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a77b5bf08b4807fae6be540490951cd5084ffac2ed9b3692b8328f6e71a774bf","family_id":"qf-mod29-filtration-qualification","seed":202610295020,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0021","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f451eb8c08135a042867b1a3505de21ef6f5e2db29b789f9457e097f4f19e8ea","family_id":"qf-mod29-filtration-qualification","seed":202610295021,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,0,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 0, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 1, 3]], No)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [[2, 0, 3], [2, 1, 3]], No)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0022","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5de8905da4b7c7bd9d72a58cfce956f4b760be34f77749a57df1a01599fb80d3","family_id":"qf-mod29-filtration-qualification","seed":202610295022,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0023","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b72bc9d83d8e58ec2280aedc6942aa84ea9f7cca5366135eb8cfb0b4533f2d6","family_id":"qf-mod29-filtration-qualification","seed":202610295023,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0024","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ed0ca5da951b8ebe3c108a2912785eb5bab550552fb000bbe76d3ce5c203b93","family_id":"qf-mod29-filtration-qualification","seed":202610295024,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0025","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dfdeebc16d52bfd82f63a0b2b055a034b02d78d750deed87d477bcc621bbceb3","family_id":"qf-mod29-filtration-qualification","seed":202610295025,"semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]]}"},"fields":{"title":"Later Information Must Refine Earlier Information","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Give (n,time_count,nesting_failures,filtration?). Failure rows [t,a,b] list t increasingly, then a<b increasingly, when outcomes share a block at t but belonged to different blocks at t−1.","answer":{"kind":"expression","value":"(6, 3, [], Yes)","explanation":"Compare all carrier pairs at every adjacent time. A later merger across previously distinct blocks is a nesting failure, whatever numerical names the block labels use. The exact result, retaining the requested order, is (6, 3, [], Yes)."},"skills":["Later Information Must Refine Earlier Information"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0026","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a13b50c2ce442d31e5d12d1b6427923214b193f3665080ca65f346a45cb4941","family_id":"qf-mod29-filtration-block-at-time","seed":202610295026,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=0. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 0, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0027","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b86bb0d536fc54f768409f6648024717525174af2711605f7cdfba4a712e7d4","family_id":"qf-mod29-filtration-block-at-time","seed":202610295027,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=1. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 1, [0, 1, 2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0028","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ff91539ab27d3fbb1a7a649e53845fd1d7a2e31e8c1735f299cba948b144aa89","family_id":"qf-mod29-filtration-block-at-time","seed":202610295028,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=2. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 2, [0, 2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 2, [0, 2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0029","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ecb06950aef4a199e473924964f3aaeb93eb2115470e878870725ba27a29713","family_id":"qf-mod29-filtration-block-at-time","seed":202610295029,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=3. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 3, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0030","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cd3aa197add3202e7fb702011627d675b55444b64d5e8d9c0fd410934130a3fe","family_id":"qf-mod29-filtration-block-at-time","seed":202610295030,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=4. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 4, [3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0031","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c8b4cf66d40d0065c1503cd4e76ab4be8d90d02da3872a85212bb8519f207ec","family_id":"qf-mod29-filtration-block-at-time","seed":202610295031,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=5. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 5, [3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 5, [3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0032","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bac4117570476b046a10636c7d14ee7ceec0d9fac23065d875dc4304d6b79a32","family_id":"qf-mod29-filtration-block-at-time","seed":202610295032,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=0. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 0, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0033","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5cf397c9479ac2335abb78493d1bcbbefa09045ba0934f2fde9e02a27f28fc9","family_id":"qf-mod29-filtration-block-at-time","seed":202610295033,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=1. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 1, [0, 1, 2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0034","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89aca9e8dce262f7afc498c75318b4d0f05751f74cdb4b291615805a19a52b38","family_id":"qf-mod29-filtration-block-at-time","seed":202610295034,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=2. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 2, [0, 1, 2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 2, [0, 1, 2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0035","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e3098edae6d62ea42cac27b514867e1ce90939b9f9c6d95e3bb6c0a1f455783f","family_id":"qf-mod29-filtration-block-at-time","seed":202610295035,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=3. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 3, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0036","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d705f7b1577d672b8a02212237e772e351e36bd376f37b8ba59ef52c4a54f1ee","family_id":"qf-mod29-filtration-block-at-time","seed":202610295036,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=4. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 4, [3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0037","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e5013dd4028360ac5929acb9c59f59dd21fb53d04cf0bd156f5a2cb450a7aa7e","family_id":"qf-mod29-filtration-block-at-time","seed":202610295037,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=5. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 5, [4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 5, [4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0038","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cdd244e8c1a8fe3613bb74332e4cf096fa7b7e6286ae218d417d514fb0499684","family_id":"qf-mod29-filtration-block-at-time","seed":202610295038,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=0. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 0, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0039","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ae1f341c74b0f6815bd9e859bb89f7457ebc90f590bb7158f3ef861512be614","family_id":"qf-mod29-filtration-block-at-time","seed":202610295039,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=1. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 1, [0, 1, 2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0040","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6393144aa474aa79f2cf9f91d109036cd32b8d80d87034179f3cd4cb78bd0dc","family_id":"qf-mod29-filtration-block-at-time","seed":202610295040,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=2. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 2, [1, 2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 2, [1, 2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0041","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"43b4693160452505b9ee240dc83705ab6937395454a369ab24a4c1ee5537814f","family_id":"qf-mod29-filtration-block-at-time","seed":202610295041,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=3. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 3, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0042","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"378ba7de43947ada8f6706b37ca2d11cb6e47a187290ae992c9952037722bc40","family_id":"qf-mod29-filtration-block-at-time","seed":202610295042,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=4. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 4, [3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0043","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b3a49d605a83b4f864e6c36e36374b693b1b7eb0f0c708c33b79dd34a0653d7","family_id":"qf-mod29-filtration-block-at-time","seed":202610295043,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=5. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 5, [3, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 5, [3, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0044","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b295ef67ab7cd470cd0ec7d779a3753dba208614ac20861e4accb4c123043a5b","family_id":"qf-mod29-filtration-block-at-time","seed":202610295044,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=0. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 0, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0045","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6919aa056b789f7408dde5d479c8af34ccad5885fa998e24176b212935b7b37e","family_id":"qf-mod29-filtration-block-at-time","seed":202610295045,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=1. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 1, [0, 1, 2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0046","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ff94f0a9cdf5876381695839c58451246cbd875e3fd3228366caf383a523aea","family_id":"qf-mod29-filtration-block-at-time","seed":202610295046,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=2. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 2, [2])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 2, [2])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0047","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9297d76b1c6579e55516c3460f389432caa228364e27a380657a5d3be4d9572b","family_id":"qf-mod29-filtration-block-at-time","seed":202610295047,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=3. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 3, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0048","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"816f3a01692c7a22bd6cc9bf90e7b269d1cdc7bc48826c350b78de96cc7aae7b","family_id":"qf-mod29-filtration-block-at-time","seed":202610295048,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"time\":1}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, outcome=4. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (1, 4, [3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0049","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40040b974aae4711815f69405fbd4dbbd4ab777b9f8115410e5a3febcaa6f023","family_id":"qf-mod29-filtration-block-at-time","seed":202610295049,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"time\":2}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, outcome=5. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(2, 5, [3, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (2, 5, [3, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0050","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b05f52178d1a6825e4b79b1d4be337bad54f3baa949ce5e5a52fa3e0e68950c","family_id":"qf-mod29-filtration-block-at-time","seed":202610295050,"semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"time\":0}"},"fields":{"title":"Read One Information Block without Assuming All-Time Qualification","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, outcome=0. Give (time,outcome,information_block).","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation":"Find every outcome with the same label in the selected partition row and list the outcome indices increasingly. This is a block lookup, not by itself a certificate that all partitions form a filtration. The exact result, retaining the requested order, is (0, 0, [0, 1, 2, 3, 4, 5])."},"skills":["Read One Information Block without Assuming All-Time Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0051","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8adaa533f828b66cee5eadef8bc1381de7fcc951a85dd44c9f25c5d5a4af65ab","family_id":"qf-mod29-filtration-adaptedness","seed":202610295051,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,2,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 2, 1, 2, 2, 2], [2, 2, 2, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0052","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"abdde4ab44588855834b9f3c1d962bff28ca139f66afbddc8833fe9f1a165612","family_id":"qf-mod29-filtration-adaptedness","seed":202610295052,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 2, 2, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0053","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"645c0eded66707daee7eaf690764b5f18c27dcc4eb93e8e6d428e82c1c5ddf7f","family_id":"qf-mod29-filtration-adaptedness","seed":202610295053,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 3, 2, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0054","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1caf63104ce8775fd4dff8f033470774d0cde64cf0c97142b022992bfc95fd43","family_id":"qf-mod29-filtration-adaptedness","seed":202610295054,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 3, 2, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0055","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0b021446e633138ca95079e8e259be70df63e1ac8da912210392d2b956f6092","family_id":"qf-mod29-filtration-adaptedness","seed":202610295055,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 2, 3, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0056","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"62fe97fbad5d747631ae85a666d53cd2e7262451b2774e98299fbf6a1b633c24","family_id":"qf-mod29-filtration-adaptedness","seed":202610295056,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,2,3,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 2, 1, 2, 2, 2], [3, 2, 3, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0057","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"884fb007902d4e6a89874bef2198484e91acdf92903a1e02dd6bfa4774349df6","family_id":"qf-mod29-filtration-adaptedness","seed":202610295057,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 3, 3, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0058","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"142ab64841c6f7cd001e610105dc080a2ae6258834f1e4868c0f654e41cbcc1e","family_id":"qf-mod29-filtration-adaptedness","seed":202610295058,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 3, 3, 12, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0059","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9862440509aa8813d2f593f5c0514a5ef3f74199665e6133ab78f0749b25431c","family_id":"qf-mod29-filtration-adaptedness","seed":202610295059,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 2, 2, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0060","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b25e24fdf5632d93af0f9f9c6a2eb8e4c79cb1e94c27e890c5f451c70a5727c0","family_id":"qf-mod29-filtration-adaptedness","seed":202610295060,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 2, 2, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0061","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"952357b9325c6b25b32ca8e2f3b44c27cd5a2d98762c8e8f4812bf9075ef4084","family_id":"qf-mod29-filtration-adaptedness","seed":202610295061,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,3,2,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 2, 1, 2, 2, 2], [2, 3, 2, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0062","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e025c38d69ad2831e48a062ea06c0edb3374d78e57ce44e009f338e6f500e9f4","family_id":"qf-mod29-filtration-adaptedness","seed":202610295062,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 3, 2, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0063","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a9e16a1bb9da36d31f06a3d0fc33f5137d003c3d220c3f44388736a36c742e18","family_id":"qf-mod29-filtration-adaptedness","seed":202610295063,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 2, 3, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0064","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3513219225ed723f61439b62b8d9d9bf3a51cba99594a787282c942702703c8b","family_id":"qf-mod29-filtration-adaptedness","seed":202610295064,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 2, 3, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0065","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cb60b62b12be76ec926a0332c468faeb0b35cefbe8f70d60769fa794032e788f","family_id":"qf-mod29-filtration-adaptedness","seed":202610295065,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 3, 3, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0066","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"824c157fd1daecfcb1bbf856ac08cfcd142166c7a523f4d088fc0e026168b1cf","family_id":"qf-mod29-filtration-adaptedness","seed":202610295066,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,3,3,13,12,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 2, 1, 2, 2, 2], [3, 3, 3, 13, 12, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0067","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0419c46d9cbf24ef9ac3876e20263280d7f814b5b3e06081c6101c56f2e8b637","family_id":"qf-mod29-filtration-adaptedness","seed":202610295067,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 2, 2, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0068","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a211c4a99803085b69bc3d51fb2d85bd6c8dbbcb9371f710145a6b9a9893221a","family_id":"qf-mod29-filtration-adaptedness","seed":202610295068,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 2, 2, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0069","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"048c615563e04ec0ccd18781f7da4ea657ae1b5e12597265611922adee845432","family_id":"qf-mod29-filtration-adaptedness","seed":202610295069,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 3, 2, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0070","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e399b70e3bb5c64d5b2cd902599427e57f61c8d408fa78e9b5c37060265fa7a8","family_id":"qf-mod29-filtration-adaptedness","seed":202610295070,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 3, 2, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0071","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e83e692dee698745442c4532032ced7ce4487f774c2d63ea0ecc9e9d756deb65","family_id":"qf-mod29-filtration-adaptedness","seed":202610295071,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,3,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 2, 1, 2, 2, 2], [2, 2, 3, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0072","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c08a6860d4b17e9f7ad7ddc78c619401b840f95a316f21a979016804bc3ff081","family_id":"qf-mod29-filtration-adaptedness","seed":202610295072,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 2, 3, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0073","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12d31537dcae69fd0225260d4cef0e83781a5d25c6ab565cccb64200e0cf522b","family_id":"qf-mod29-filtration-adaptedness","seed":202610295073,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 3, 3, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0074","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9502f645b9bc58630f0b091d9c7f4c232ea6964be9e6dec990fdd3844d4c517","family_id":"qf-mod29-filtration-adaptedness","seed":202610295074,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [3, 3, 3, 12, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0075","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3ebe02d44a97f2edb5e32d46870c64bbcc7c073201dd4307eb6b69eb243e2f55","family_id":"qf-mod29-filtration-adaptedness","seed":202610295075,"semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,13,12]]}"},"fields":{"title":"Process Measurability Is Separate from Information Nesting","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. Complete time-aligned process_values=[[0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, 2], [2, 2, 2, 13, 13, 12]]. Give (filtration?,measurability_failures,adapted?,qualified_adapted_process?). Failure rows are [time,block_label,indices,distinct_values], traversing times and first-seen block labels in row order.","answer":{"kind":"expression","value":"(Yes, [], Yes, Yes)","explanation":"Test whether the process is constant on every information block at each time. The adapted flag here records these measurability checks; the final qualified flag additionally requires the partition sequence to be a filtration. Information nesting alone does not supply adaptedness. The exact result, retaining the requested order, is (Yes, [], Yes, Yes)."},"skills":["Process Measurability Is Separate from Information Nesting"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0076","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"15588282e7f7545ffaf6841e6f3a7504dfd010fe5af91a7ea42c9252eec93985","family_id":"qf-mod29-filtration-event-measurability","seed":202610295076,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0], No, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0], No, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0077","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45413c93c2621910cd612f11a69e0d041815dead54a7fe1357038bd695e06a23","family_id":"qf-mod29-filtration-event-measurability","seed":202610295077,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[0, 1, 2]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0078","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ff8b9f00658ab0191a5ae39b558db62424eb1d56b56a5bd1f5e57a1b0ad455bd","family_id":"qf-mod29-filtration-event-measurability","seed":202610295078,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[0, 2]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [0, 2], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [0, 2], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0079","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6d258b0583d248c5bd274a8d8519b04141f7d2f32223f396f1ccbe6df67a9f2b","family_id":"qf-mod29-filtration-event-measurability","seed":202610295079,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0, 1, 2, 3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0080","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d4739721c2925a12cdf1c0f5769183dcb92a4da7e7f258e29152143729c57cd","family_id":"qf-mod29-filtration-event-measurability","seed":202610295080,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[3]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [3], No, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [3], No, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0081","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57a2f7c14cb2296c47626710e36bff171ccd751108b57d39f5b77bdf8d0f9822","family_id":"qf-mod29-filtration-event-measurability","seed":202610295081,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0082","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f203b3c80ea1bf9bc8281070f77b5f71b8e1b7f7e084671c233f06b2a6d2cd3","family_id":"qf-mod29-filtration-event-measurability","seed":202610295082,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0, 1, 2, 3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0083","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"279af2201208d639821bd07088b5d5a99b7cdeb8927c52bc11f902ce020e7edc","family_id":"qf-mod29-filtration-event-measurability","seed":202610295083,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[0, 1, 2]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0084","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96690af73325a82724adf394d6afea8140c44f27c94c4e03d18f47f96a2cd855","family_id":"qf-mod29-filtration-event-measurability","seed":202610295084,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[0]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [0], No, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [0], No, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0085","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3cf2a23af549325d9bfc2fe9ca9aab7dcefefb3a1a5708daa9107b420364d8e1","family_id":"qf-mod29-filtration-event-measurability","seed":202610295085,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0, 1, 2, 3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0086","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f869447f20ebee0bce4d05716196626704b783cbc59c372e535ef62dc3e739db","family_id":"qf-mod29-filtration-event-measurability","seed":202610295086,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0087","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95af031c0b668d994d434c26541663535c987682caa89441545680b34901b23f","family_id":"qf-mod29-filtration-event-measurability","seed":202610295087,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0088","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d6e6c8452ff5020f988a9c94a787780d99913c52e2b4ee24c8defb7c1bfdfa6","family_id":"qf-mod29-filtration-event-measurability","seed":202610295088,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0], No, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0], No, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0089","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"539b930a9b5fff1cee0031737c64f8e386aa9fd7215c1d0055f8ced13b8daeab","family_id":"qf-mod29-filtration-event-measurability","seed":202610295089,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[0, 1, 2]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0090","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c44fecd0673565614ca8941405c9fec4ea3e19b5f897393cf06ba7c0556bc833","family_id":"qf-mod29-filtration-event-measurability","seed":202610295090,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[1, 2]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [1, 2], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [1, 2], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0091","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d95b08630f8bb12d959029cddddd8ce2d92a8a629bc8a3fe734a36e4a89c07c","family_id":"qf-mod29-filtration-event-measurability","seed":202610295091,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 11, 10, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0, 1, 2, 3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0092","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b6b28cb955b5c1c9748795ce64c1128f2190b8c2598081af8db044ac591656e8","family_id":"qf-mod29-filtration-event-measurability","seed":202610295092,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[3]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [3], No, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [3], No, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0093","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"821acf2ae63c60d3cf941626599943a216e1fbeb658c7fd8a66fd69b80182b44","family_id":"qf-mod29-filtration-event-measurability","seed":202610295093,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[3, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [3, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [3, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0094","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9927958274f6a5e5c0d9e8c03276e79948151ac16b9050a7222091b995241017","family_id":"qf-mod29-filtration-event-measurability","seed":202610295094,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0, 1, 2, 3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0095","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"58e28aea71756bf604156eb12b9b41f6a0dcb8ea7c91e2301a64c6f3238a6990","family_id":"qf-mod29-filtration-event-measurability","seed":202610295095,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 0, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[0, 1, 2]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0096","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9c9abacb6e9f18780a1484e8291ac157d25c954a72bd2bf22667ea9a50aaa56","family_id":"qf-mod29-filtration-event-measurability","seed":202610295096,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[2]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [2], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [2], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0097","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d14b78b09f518cc3741e28d86ce3f00c9edd3dcef28261dd6c57239520460af5","family_id":"qf-mod29-filtration-event-measurability","seed":202610295097,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0, 1, 2, 3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0098","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"693e26b2f4f91d327e133934163b330c1eb794e3d55c7e76019296fd403ef1a3","family_id":"qf-mod29-filtration-event-measurability","seed":202610295098,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"time\":1}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=1, event=[3, 4, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(1, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (1, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0099","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f7c9cbf768a11c206984cf715dcae0422df44241825a713ef3f07568bd50018","family_id":"qf-mod29-filtration-event-measurability","seed":202610295099,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"time\":2}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 1, 1, 10, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=2, event=[3, 5]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(2, [3, 5], Yes, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (2, [3, 5], Yes, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-20261029-r05-finite-filtration-0100","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f30067a926170310d515ecd4bb6c7e053bd4b7ee6bb7dab323667e5509ab8916","family_id":"qf-mod29-filtration-event-measurability","seed":202610295100,"semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"time\":0}"},"fields":{"title":"A Measurable Event Is a Union of Whole Current Blocks","stem":"Use the same finite carrier Fin(6)={0,…,5} at all times, with complete partitions=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 11, 11, 10]] in time order starting at 0. Equal labels in one row mean the same information block; numerical label size and labels in other rows carry no extra meaning. A filtration requires every later partition to refine its predecessor. Event measurability and process adaptedness are separate checks; no natural-filtration, independence or Markov conclusion is inferred. time=0, event=[0]. Normalize the event as increasing distinct outcome indices. Give (time,event,measurable?,event_must_be_union_of_time_blocks).","answer":{"kind":"expression","value":"(0, [0], No, event_must_be_union_of_time_blocks)","explanation":"Every current block must be wholly inside or wholly outside the event. Partial inclusion fails. This event check alone does not establish filtration qualification over time. The exact result, retaining the requested order, is (0, [0], No, event_must_be_union_of_time_blocks)."},"skills":["A Measurable Event Is a Union of Whole Current Blocks"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}