Use source carrier=[0, 1, 2], target carrier=[0, 1], aligned mapping=[0, 1, 0], source yes-set=[1], target yes-set=[1]. Sort domain values with their associated images, not independently. A null or outside image is not a total map. Target decider truth table=[false, true], aligned with the supplied target carrier. Mode=valid_transfer. Give (mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary).
G001 — Use source carrier=[0, 1, 2], target carrier=[0, 1], aligned mapping=[0, 1, 0], source yes-set=[1], target yes-set=[1]. Sort domain values with their associated images, not independently. A null or outside image is not a total map. Target decider truth table=[false, true], aligned with the supplied target carrier. Mode=valid_transfer. Give (mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary).
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.
List the full source field order without JavaScript.Original modes select contract6/4/6/6 and IVT8/7/8 roles,without padding or answer-shape inference.
Sort source values numerically with their aligned images,and target values numerically.Null,outside and Boolean images are not valid integer target values;False is not0.Qualification retains actual raw images and the first invalid row,not an invented total map.
derived = [[[0, No, 0, No, Yes], [1, Yes, 1, Yes, Yes], [2, No, 0, No, Yes]], Yes, Yes]
Conditions: none
For every x audit x in A iff f(x) in B,in both yes and no directions.Invalid images have null target predicates,notFalse.Totality and full membership equivalence jointly qualify this finite reduction.
Align the exact Boolean decider with ORIGINAL target values before reordering.Construct A only for a total map;partial gives null.reverse_misuse may construct a correct A table while rejecting reverse use.Yes-only may be partial/vacuous;do not add a totality premise.Finite tables certify these domains,not infinite computability.
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
(valid_transfer, [[0, No, 0, No, Yes], [1, Yes, 1, Yes, Yes], [2, No, 0, No, Yes]], Yes, Yes, [No, Yes], Yes, [No, Yes, No], Yes, Yes, No, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)
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.