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R0051-26179 · q-20261015-advance-20261115-r07-many-one-reduction-0004
Use source carrier=[0, 1, 2, 3, 4, 5], target carrier=[0, 1, 2], aligned mapping=[0, 1, 2, 0, 1, 2]. Sort domain values with their associated images, not independently. A null or outside image is not a total map. Give (source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate).
G001 — Use source carrier=[0, 1, 2, 3, 4, 5], target carrier=[0, 1, 2], aligned mapping=[0, 1, 2, 0, 1, 2]. Sort domain values with their associated images, not independently. A null or outside image is not a total map. Give (source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate).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
source roles = [mreduction-total-map-qualification]
After
derived = [[source_carrier, target_carrier, mapping_rows, total, first_invalid_image_or_null, certificate]]
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.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [Reduction ORIGINAL map, [0, 1, 2, 3, 4, 5], [0, 1, 2], [0, 1, 2, 0, 1, 2]]
After
derived = [[0, 1, 2, 3, 4, 5], [0, 1, 2], [0, 1, 2, 0, 1, 2], [[0, 0, Yes], [1, 1, Yes], [2, 2, Yes], [3, 0, Yes], [4, 1, Yes], [5, 2, 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.
Rule: Reduction_original_domain_IMAGE_pairs_sorted_together_STRICT_types · Uses: G001, S001
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.([0, 1, 2, 3, 4, 5], [0, 1, 2], [[0, 0, Yes], [1, 1, Yes], [2, 2, Yes], [3, 0, Yes], [4, 1, Yes], [5, 2, Yes]], Yes, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)
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: 77487e5f72450a6c014cea573b19663663d2339183361faf0c4d4d88aeb017d7candidate record SHA-256: 60f0a188a33858532b10cda7e97cba64e7ba91e738b4fd6ea3ffe966ae54e592semantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5cLean: NOT_RUN · human review: NOT_PERFORMED