Original question and givens
Use source carrier=[0, 1, 2, 3, 4, 5, 6, 7, 8], target carrier=[0, 1], aligned mapping=[0, 1, 0, 1, 0, 1, 0, 1, null], source yes-set=[1, 3, 5, 7], 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=partial_map. 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, 3, 4, 5, 6, 7, 8], target carrier=[0, 1], aligned mapping=[0, 1, 0, 1, 0, 1, 0, 1, null], source yes-set=[1, 3, 5, 7], 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=partial_map. 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).
Step-by-step derivation
S001 · implies
Before
source roles = [mreduction-decider-transfer-boundary]
After
derived = [[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]]
Conditions: none
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.
Step identifiers and dependencies
Rule: source_ordered_fields_without_JS · Uses: G001
S002 · implies
Before
source roles = [Reduction ORIGINAL map, [0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1], [0, 1, 0, 1, 0, 1, 0, 1, null]]
After
derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1], [0, 1, 0, 1, 0, 1, 0, 1, null], [[0, 0, Yes], [1, 1, Yes], [2, 0, Yes], [3, 1, Yes], [4, 0, Yes], [5, 1, Yes], [6, 0, Yes], [7, 1, Yes], [8, null, No]], No, [8, null, No]]
Conditions: none
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.
Step identifiers and dependencies
Rule: Reduction_original_domain_IMAGE_pairs_sorted_together_STRICT_types · Uses: G001, S001
S003 · implies
Before
source roles = [Reduction ORIGINAL map, [1, 3, 5, 7], [1], [0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1], [0, 1, 0, 1, 0, 1, 0, 1, null]]
After
derived = [[[0, No, 0, No, Yes], [1, Yes, 1, Yes, Yes], [2, No, 0, No, Yes], [3, Yes, 1, Yes, Yes], [4, No, 0, No, Yes], [5, Yes, 1, Yes, Yes], [6, No, 0, No, Yes], [7, Yes, 1, Yes, Yes], [8, No, null, null, No]], No, No]
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.
Step identifiers and dependencies
Rule: Reduction_EVERY_yes_AND_no_membership_IFF_not_yes_only · Uses: G001, S002
S004 · implies
Before
source roles = [partial_map, [0, 1], [No, Yes], [[0, No, 0, No, Yes], [1, Yes, 1, Yes, Yes], [2, No, 0, No, Yes], [3, Yes, 1, Yes, Yes], [4, No, 0, No, Yes], [5, Yes, 1, Yes, Yes], [6, No, 0, No, Yes], [7, Yes, 1, Yes, Yes], [8, No, null, null, No]]]
After
derived = [[0, 1], [No, Yes], Yes, null, No, No, No]
Conditions: none
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.
Step identifiers and dependencies
Rule: Reduction_original_TARGET_decider_alignment_FORWARD_transfer_mode_boundary · Uses: G001, S003
Result
(partial_map, [[0, No, 0, No, Yes], [1, Yes, 1, Yes, Yes], [2, No, 0, No, Yes], [3, Yes, 1, Yes, Yes], [4, No, 0, No, Yes], [5, Yes, 1, Yes, Yes], [6, No, 0, No, Yes], [7, Yes, 1, Yes, Yes], [8, No, null, null, No]], No, No, [No, Yes], Yes, null, No, No, 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.