Complete Information Refinement, Separate Adaptedness and Measurable Events
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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Finite filtration · qf-mod29-filtration-event-measurability · candidate
Canonical question JSONL · English JSONL · Validation report