Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-1, 12], candidate=[13, -2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).
G001 — Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-1, 12], candidate=[13, -2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).
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.
density14/15 use FULL-prefix underscores;density17 uses LOCAL hyphens.The coordinate and circle frames differ.Retain THIS family ordered answer roles/types and all original bilingual JSON/status.
Coordinate swap candidate minus expected ORIGINAL P minus Q coordinate0 := sub(13, 12)
After
Coordinate swap candidate minus expected ORIGINAL P minus Q coordinate0 = 1
Conditions: none
Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations.
Coordinate swap candidate minus expected ORIGINAL P minus Q coordinate1 := sub(-2, -1)
After
Coordinate swap candidate minus expected ORIGINAL P minus Q coordinate1 = -1
Conditions: none
Use ORIGINAL operands for exact integer/rational arithmetic.Only RAW inputs use SAFE or the explicit family bounds;derived values do not inherit those caps or use floating approximations.
THIS coordinate protocol retains both signs of ORIGINAL P-Q,OPPOSITE the length bank Q-P.A component difference is not distance or rendered size;derived values may exceed SAFE.
Expected is the ORIGINAL field swap(y,x),with residual candidate-expected.Candidate agreement and whether ORIGINAL P is a fixed point are SEPARATE flags.This data-field operation is not a formal reflection bridge.
S005 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.
S004 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.
S003 · premise_and_result_audit — Recompute Coordinate swap candidate minus expected ORIGINAL P minus Q coordinate1 with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute Coordinate swap candidate minus expected ORIGINAL P minus Q coordinate0 with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.
Result
([12, -1], [1, -1], No, No)
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.