Use exact rational absolute values embedded in R; negative representation denominators are normalized before deciding signs. x=9/-3. Give (reduced x, nonnegative or negative branch, abs(x)); zero belongs to the nonnegative branch.
G001 — Use exact rational absolute values embedded in R; negative representation denominators are normalized before deciding signs. x=9/-3. Give (reduced x, nonnegative or negative branch, abs(x)); zero belongs to the nonnegative branch.
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.
Retain the ORIGINAL bank full operation prefix,domain and ordered answer roles.Use orthogonal_equal_unit only where a frame is declared,and degrees where an angle unit is declared.Integer fractions retain/1.Do not invent parameters or alter original bilingual sources.
Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap.
Absolute x ORIGINAL negative branch negation := sub(0, -3)
After
Absolute x ORIGINAL negative branch negation = 3
Conditions: none
Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap.
Return normalized x,the branch LABEL chosen by its VALUE,and abs(x).Zero belongs to the nonnegative branch,and a negative denominator does not mean a negative value.This is the declared rational slice,not a new certificate for all real absolute-value properties.
S005 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
S004 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
S003 · premise_and_result_audit — Recompute Absolute x ORIGINAL negative branch negation with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
S001 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
Result
(-3/1, negative, 3/1)
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.