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R0068-34839 · q-20260920-rational-valid-representation-0014
Both p=1 and q=7 are explicitly integers. Is p/q a valid rational-number representation?
G001 — Both p=1 and q=7 are explicitly integers. Is p/q a valid rational-number representation?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-valid-representation, [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 = [1, 7]
After
derived = [Yes]
Conditions: none
A rational representation needs INTEGER p,q and q≠0.Zero denominator is a LEGAL No,including0/0.This branch does NOT divide or fabricate a numeric value.
Rule: Rational_RAW_integer_pair_NONzero_DEN_before_any_division · 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.Yes
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: 8d7c0a2be5c4cd1ac92f75f0318011f12b168a29c94a829d17173e29757c61eecandidate record SHA-256: f9c8312baf8046cd38302e171c0035e5f6e9da909fe357abb27bbbef77bd07c6semantic review receipt SHA-256: e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066edquestion-first witness SHA-256: 8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229Lean: NOT_RUN · human review: NOT_PERFORMED