# Complete Information Refinement, Separate Adaptedness and Measurable Events

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261014-advance-20261029-r05-finite-filtration-foundations · 2026-10-14 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0001/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 2. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0002/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 3. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0003/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 4. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0004/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 5. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0005/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 6. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [[2, 0, 3], [2, 2, 3]], No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0006/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 7. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0007/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 8. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0008/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 9. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0009/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 10. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0010/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 11. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [[2, 0, 3], [2, 2, 3]], No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0011/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 12. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0012/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 13. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0013/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 14. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0014/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 15. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0015/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 16. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0016/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 17. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0017/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 18. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0018/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 19. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0019/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 20. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0020/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 21. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [[2, 0, 3], [2, 1, 3]], No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0021/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 22. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0022/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 23. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0023/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 24. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0024/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 25. Later Information Must Refine Earlier Information

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.

View answer and explanation(6, 3, [], Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0025/)

Finite filtration · qf-mod29-filtration-qualification · candidate





## 26. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 0, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0026/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 27. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 1, [0, 1, 2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0027/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 28. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 2, [0, 2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0028/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 29. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 3, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0029/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 30. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 4, [3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0030/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 31. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 5, [3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0031/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 32. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 0, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0032/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 33. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 1, [0, 1, 2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0033/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 34. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 2, [0, 1, 2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0034/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 35. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 3, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0035/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 36. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 4, [3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0036/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 37. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 5, [4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0037/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 38. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 0, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0038/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 39. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 1, [0, 1, 2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0039/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 40. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 2, [1, 2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0040/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 41. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 3, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0041/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 42. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 4, [3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0042/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 43. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 5, [3, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0043/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 44. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 0, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0044/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 45. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 1, [0, 1, 2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0045/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 46. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 2, [2])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0046/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 47. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 3, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0047/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 48. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(1, 4, [3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0048/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 49. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(2, 5, [3, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0049/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 50. Read One Information Block without Assuming All-Time Qualification

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).

View answer and explanation(0, 0, [0, 1, 2, 3, 4, 5])

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]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0050/)

Finite filtration · qf-mod29-filtration-block-at-time · candidate





## 51. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0051/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 52. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0052/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 53. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0053/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 54. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0054/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 55. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0055/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 56. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0056/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 57. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0057/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 58. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0058/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 59. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0059/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 60. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0060/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 61. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0061/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 62. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0062/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 63. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0063/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 64. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0064/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 65. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0065/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 66. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0066/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 67. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0067/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 68. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0068/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 69. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0069/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 70. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0070/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 71. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [[1, 0, [0, 1, 2], [1, 2]]], No, No)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0071/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 72. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0072/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 73. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0073/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 74. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0074/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 75. Process Measurability Is Separate from Information Nesting

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.

View answer and explanation(Yes, [], Yes, Yes)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0075/)

Finite filtration · qf-mod29-filtration-adaptedness · candidate





## 76. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0], No, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0076/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 77. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0077/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 78. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [0, 2], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0078/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 79. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0079/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 80. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [3], No, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0080/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 81. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0081/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 82. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0082/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 83. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0083/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 84. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [0], No, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0084/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 85. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0085/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 86. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0086/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 87. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0087/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 88. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0], No, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0088/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 89. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0089/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 90. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [1, 2], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0090/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 91. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0091/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 92. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [3], No, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0092/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 93. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [3, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0093/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 94. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0094/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 95. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [0, 1, 2], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0095/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 96. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [2], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0096/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 97. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0, 1, 2, 3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0097/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 98. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(1, [3, 4, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0098/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 99. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(2, [3, 5], Yes, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0099/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate





## 100. A Measurable Event Is a Union of Whole Current Blocks

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).

View answer and explanation(0, [0], No, event_must_be_union_of_time_blocks)

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).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261014-advance-20261029-r05-finite-filtration-0100/)

Finite filtration · qf-mod29-filtration-event-measurability · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261029-r05-finite-filtration-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261014-advance-20261029-r05-finite-filtration-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261029-r05-finite-filtration-foundations/validation-report.json)