# Question 14303: Process Measurability Is Separate from Information Nesting [Return to catalogue page 72](https://ocme.evemisslab.com/en/questions/page/72/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261014-advance-20261029-r05-finite-filtration-foundations/#q-20261014-advance-20261029-r05-finite-filtration-0053) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0027-14303 · q-20261014-advance-20261029-r05-finite-filtration-0053 ## Original question and givens Use the same 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. - 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, 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. ## 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. - [mko-finite-filtration](https://ocme.evemisslab.com/en/mko/mko-finite-filtration/) ## Step-by-step derivation S001 · impliesBefore 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, 10, 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. Step identifiers and dependenciesRule: filtration_same_carrier_time_and_label_roles · Uses: G001 S002 · impliesBefore time=1;later block label=0;indices=[0, 1, 2] After 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. Step identifiers and dependenciesRule: filtration_later_refines_earlier_complete_blocks · Uses: G001, S001 S003 · impliesBefore time=1;later block label=1;indices=[3, 4, 5] After 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. Step identifiers and dependenciesRule: filtration_later_refines_earlier_complete_blocks · Uses: G001, S002 S004 · impliesBefore time=2;later block label=0;indices=[0, 2] After 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. Step identifiers and dependenciesRule: filtration_later_refines_earlier_complete_blocks · Uses: G001, S003 S005 · impliesBefore time=2;later block label=1;indices=[1] After 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. Step identifiers and dependenciesRule: filtration_later_refines_earlier_complete_blocks · Uses: G001, S004 S006 · impliesBefore time=2;later block label=10;indices=[3, 4, 5] After 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. Step identifiers and dependenciesRule: filtration_later_refines_earlier_complete_blocks · Uses: G001, S005 S007 · impliesBefore all nesting failures in time,a,b order=[] After 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. Step identifiers and dependenciesRule: filtration_nesting_not_adaptedness · Uses: G001, S006 S008 · impliesBefore time=0;first-seen block label=0;indices=[0, 1, 2, 3, 4, 5];aligned process values=[0, 0, 0, 0, 0, 0] After distinct values in encounter order=[0];constant=Yes Conditions: none At each time the process must be constant on every information block.Order failures by time and first-seen block label,and values by first encounter rather than sorting. Step identifiers and dependenciesRule: adaptedness_every_current_block_not_nesting_alone · Uses: G001, S007 S009 · impliesBefore time=1;first-seen block label=0;indices=[0, 1, 2];aligned process values=[1, 1, 1] After distinct values in encounter order=[1];constant=Yes Conditions: none At each time the process must be constant on every information block.Order failures by time and first-seen block label,and values by first encounter rather than sorting. Step identifiers and dependenciesRule: adaptedness_every_current_block_not_nesting_alone · Uses: G001, S008 S010 · impliesBefore time=1;first-seen block label=1;indices=[3, 4, 5];aligned process values=[2, 2, 2] After distinct values in encounter order=[2];constant=Yes Conditions: none At each time the process must be constant on every information block.Order failures by time and first-seen block label,and values by first encounter rather than sorting. Step identifiers and dependenciesRule: adaptedness_every_current_block_not_nesting_alone · Uses: G001, S009 S011 · impliesBefore time=2;first-seen block label=0;indices=[0, 2];aligned process values=[2, 2] After distinct values in encounter order=[2];constant=Yes Conditions: none At each time the process must be constant on every information block.Order failures by time and first-seen block label,and values by first encounter rather than sorting. Step identifiers and dependenciesRule: adaptedness_every_current_block_not_nesting_alone · Uses: G001, S010 S012 · impliesBefore time=2;first-seen block label=1;indices=[1];aligned process values=[3] After distinct values in encounter order=[3];constant=Yes Conditions: none At each time the process must be constant on every information block.Order failures by time and first-seen block label,and values by first encounter rather than sorting. Step identifiers and dependenciesRule: adaptedness_every_current_block_not_nesting_alone · Uses: G001, S011 S013 · impliesBefore time=2;first-seen block label=10;indices=[3, 4, 5];aligned process values=[12, 12, 12] After distinct values in encounter order=[12];constant=Yes Conditions: none At each time the process must be constant on every information block.Order failures by time and first-seen block label,and values by first encounter rather than sorting. Step identifiers and dependenciesRule: adaptedness_every_current_block_not_nesting_alone · Uses: G001, S012 S014 · impliesBefore filtration=Yes;all per-time measurability failures=[] After source adapted checks pass=Yes;qualified adapted process=Yes Conditions: none Here the source adapted field records per-time measurability checks.The last field additionally needs filtration qualification;nesting and measurability do not replace one another or imply naturalness,independence or Markov behavior. Step identifiers and dependenciesRule: adapted_flag_vs_qualified_adapted_process · Uses: G001, S013 ## Reverse checks - S014 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S013 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S012 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - 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 (Yes, [], Yes, Yes) 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. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 645c0eded66707daee7eaf690764b5f18c27dcc4eb93e8e6d428e82c1c5ddf7f - candidate record SHA-256: 819962259125e7fd2be1c230e812bf19ddd94a4b4cc12e1bb9f3f2ae8ac2ebee - semantic review receipt SHA-256: e49bf5eaa968c09ebac4ad538ce58251671ed922c957cee1471cfc7b68934bfe - question-first witness SHA-256: a7976057c26051fab92342fc95d48af224466c0e1e4ab6ae4c8811c02772e6da - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261029-r05-finite-filtration-0053.json)