Use the same 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).
G001 — Use the same 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).
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
same carrier Fin(6);complete partitions in original time order=[[0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 10, 11, 10]]
After
equal labels mean same information block only within that row
Conditions: none
Labels encode equivalence blocks only within their time row.Label magnitude or reuse across rows carries no extra information;larger numbers do not mean more information.
earlier block labels in encounter order=[0];contained in one earlier block=Yes
Conditions: none
Every later block must lie wholly in one earlier block.Merging previously distinguishable outcomes violates filtration;the refinement direction cannot be reversed.
earlier block labels in encounter order=[0];contained in one earlier block=Yes
Conditions: none
Every later block must lie wholly in one earlier block.Merging previously distinguishable outcomes violates filtration;the refinement direction cannot be reversed.
earlier block labels in encounter order=[0];contained in one earlier block=Yes
Conditions: none
Every later block must lie wholly in one earlier block.Merging previously distinguishable outcomes violates filtration;the refinement direction cannot be reversed.
earlier block labels in encounter order=[0];contained in one earlier block=Yes
Conditions: none
Every later block must lie wholly in one earlier block.Merging previously distinguishable outcomes violates filtration;the refinement direction cannot be reversed.
earlier block labels in encounter order=[1];contained in one earlier block=Yes
Conditions: none
Every later block must lie wholly in one earlier block.Merging previously distinguishable outcomes violates filtration;the refinement direction cannot be reversed.
earlier block labels in encounter order=[1];contained in one earlier block=Yes
Conditions: none
Every later block must lie wholly in one earlier block.Merging previously distinguishable outcomes violates filtration;the refinement direction cannot be reversed.
filtration=Yes;per-time measurability checks remain separate
Conditions: none
Audit refinement at every adjacent time.Even if nesting fails,the protocol may still look up a block or check measurability in one row.One passing row does not repair the whole information sequence.
S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
Result
(0, 0, [0, 1, 2, 3, 4, 5])
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.