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Question 26149: Forward Decider Transfer Needs a Total Iff Reduction and a Correct Target Decider

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0051-26149 · q-20261015-advance-20261115-r07-many-one-reduction-0099

Original question and givens

Use source carrier=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], target carrier=[0, 1], aligned mapping=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], source yes-set=[0], target yes-set=[0]. Sort domain values with their associated images, not independently. A null or outside image is not a total map. Target decider truth table=[true, false], aligned with the supplied target carrier. Mode=one_way_yes_only. 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, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], target carrier=[0, 1], aligned mapping=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], source yes-set=[0], target yes-set=[0]. Sort domain values with their associated images, not independently. A null or outside image is not a total map. Target decider truth table=[true, false], aligned with the supplied target carrier. Mode=one_way_yes_only. 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.

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, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

After

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [[0, 0, Yes], [1, 0, Yes], [2, 0, Yes], [3, 0, Yes], [4, 0, Yes], [5, 0, Yes], [6, 0, Yes], [7, 0, Yes], [8, 0, Yes], [9, 0, Yes], [10, 0, Yes], [11, 0, Yes], [12, 0, Yes], [13, 0, Yes], [14, 0, Yes], [15, 0, Yes], [16, 0, Yes], [17, 0, Yes], [18, 0, Yes], [19, 0, Yes], [20, 0, Yes], [21, 0, Yes], [22, 0, Yes], [23, 0, Yes], [24, 0, Yes], [25, 0, Yes]], Yes, null]

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, [0], [0], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

After

derived = [[[0, Yes, 0, Yes, Yes], [1, No, 0, Yes, No], [2, No, 0, Yes, No], [3, No, 0, Yes, No], [4, No, 0, Yes, No], [5, No, 0, Yes, No], [6, No, 0, Yes, No], [7, No, 0, Yes, No], [8, No, 0, Yes, No], [9, No, 0, Yes, No], [10, No, 0, Yes, No], [11, No, 0, Yes, No], [12, No, 0, Yes, No], [13, No, 0, Yes, No], [14, No, 0, Yes, No], [15, No, 0, Yes, No], [16, No, 0, Yes, No], [17, No, 0, Yes, No], [18, No, 0, Yes, No], [19, No, 0, Yes, No], [20, No, 0, Yes, No], [21, No, 0, Yes, No], [22, No, 0, Yes, No], [23, No, 0, Yes, No], [24, No, 0, Yes, No], [25, No, 0, Yes, No]], Yes, 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 = [one_way_yes_only, [0, 1], [Yes, No], [[0, Yes, 0, Yes, Yes], [1, No, 0, Yes, No], [2, No, 0, Yes, No], [3, No, 0, Yes, No], [4, No, 0, Yes, No], [5, No, 0, Yes, No], [6, No, 0, Yes, No], [7, No, 0, Yes, No], [8, No, 0, Yes, No], [9, No, 0, Yes, No], [10, No, 0, Yes, No], [11, No, 0, Yes, No], [12, No, 0, Yes, No], [13, No, 0, Yes, No], [14, No, 0, Yes, No], [15, No, 0, Yes, No], [16, No, 0, Yes, No], [17, No, 0, Yes, No], [18, No, 0, Yes, No], [19, No, 0, Yes, No], [20, No, 0, Yes, No], [21, No, 0, Yes, No], [22, No, 0, Yes, No], [23, No, 0, Yes, No], [24, No, 0, Yes, No], [25, No, 0, Yes, No]]]

After

derived = [[0, 1], [Yes, No], Yes, [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], 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

Reverse checks

  • 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

(one_way_yes_only, [[0, Yes, 0, Yes, Yes], [1, No, 0, Yes, No], [2, No, 0, Yes, No], [3, No, 0, Yes, No], [4, No, 0, Yes, No], [5, No, 0, Yes, No], [6, No, 0, Yes, No], [7, No, 0, Yes, No], [8, No, 0, Yes, No], [9, No, 0, Yes, No], [10, No, 0, Yes, No], [11, No, 0, Yes, No], [12, No, 0, Yes, No], [13, No, 0, Yes, No], [14, No, 0, Yes, No], [15, No, 0, Yes, No], [16, No, 0, Yes, No], [17, No, 0, Yes, No], [18, No, 0, Yes, No], [19, No, 0, Yes, No], [20, No, 0, Yes, No], [21, No, 0, Yes, No], [22, No, 0, Yes, No], [23, No, 0, Yes, No], [24, No, 0, Yes, No], [25, No, 0, Yes, No]], Yes, No, [Yes, No], Yes, [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], 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.

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: 527479585ad1a91418ed5100add9da20a9703fd466fa687cae3b0dfef9f3b512
  • candidate record SHA-256: 6a9aeb978e89690ffe733aa090cb5be2caf53e9f699fc87d3e1d92639b8136e4
  • semantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3
  • question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5c
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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