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R0068-34772 · q-20260920-rational-denominator-sign-normalization-0022
Normalize 9/-4 to an exact representation with a positive denominator.
G001 — Normalize 9/-4 to an exact representation with a positive denominator.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 = [qf-rational-denominator-sign-normalization, [p, q]]
After
derived = [BASE-no-required-operation, no-invented-domain]
Conditions: none
Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact.
Rule: R68_BANK_specific_keys_operations_and_numeric_guards · Uses: G001
Before
source roles = [9, -4]
After
derived = [-9, 4, -9/4]
Conditions: none
ONLY when the denominator is negative,multiply BOTH components by−1.This task DOES NOT REDUCE:2/2,0/4,−2/6 may be correct sign-only answers.A positive denominator leaves the original representation unchanged.Do not silently substitute lowest terms.
Rule: Rational_SIGN_ONLY_simultaneous_sign_flip_NO_gcd_reduction · Uses: G001, S001
S002 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.S001 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.-9/4
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: 696095d22185845990be1c656bbcdf616ac27d70bf53469860d2e6c27ac8ea0fcandidate record SHA-256: 97a6e2ee76556cd8117dccc38b5d6045002137bf1b1dff9a441fe271e5b7f5e2semantic review receipt SHA-256: e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066edquestion-first witness SHA-256: 8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229Lean: NOT_RUN · human review: NOT_PERFORMED