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R0016-08730 · q-20261013-advance-20261018-r06-decision-problem-0055
The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).
G001 — The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).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.
Before
domain Fin(6);raw yes instances=[2]
After
normalized yes set=[2]
Conditions: none
Keep the yes-instance specification separate from the candidate decider.Deduplicate labels as a set and reject outside-domain labels.A complete finite table does not prove an arbitrary program decidable or terminating on infinite inputs.
Rule: finite_decision_spec_not_program_execution · Uses: G001
Before
input=0;spec=No;declared decider=Yes
After
mismatch=Yes
Conditions: none
Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.
Rule: finite_decision_each_decider_cell · Uses: G001, S001
Before
input=1;spec=No;declared decider=No
After
mismatch=No
Conditions: none
Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.
Rule: finite_decision_each_decider_cell · Uses: G001, S002
Before
input=2;spec=Yes;declared decider=Yes
After
mismatch=No
Conditions: none
Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.
Rule: finite_decision_each_decider_cell · Uses: G001, S003
Before
input=3;spec=No;declared decider=No
After
mismatch=No
Conditions: none
Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.
Rule: finite_decision_each_decider_cell · Uses: G001, S004
Before
input=4;spec=No;declared decider=No
After
mismatch=No
Conditions: none
Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.
Rule: finite_decision_each_decider_cell · Uses: G001, S005
Before
input=5;spec=No;declared decider=No
After
mismatch=No
Conditions: none
Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.
Rule: finite_decision_each_decider_cell · Uses: G001, S006
Before
raw retained subset=[1, 4, 5];all mismatch labels=[0]
After
retained labels=[1, 4, 5];restricted yes=[];restricted mismatches=[];agreement=Yes
Conditions: none
Keep original labels under restriction and restrict both yes instances and mismatch witnesses.An excluded mismatch is not a restricted-domain witness,but the original full audit is retained.
Rule: decision_restriction_preserves_original_labels · Uses: G001, S007
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.(6, [1, 4, 5], [], [], Yes)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 2f823622cbe32d718ae22e6515af6a7b0ec5dd6fa0864ec8cb0b1206308bfd6bcandidate record SHA-256: 498a32416a923a4383836f76357e058b43cfa3f2346686f2eda2643a6498a5a9semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1Lean: NOT_RUN · human review: NOT_PERFORMED