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R0056-28626 · q-20261005-advance-20261006-r03-rate-of-change-0026
The proposed permitted endpoint inputs are x0=0 and x1=0. Is their difference a valid nonzero denominator for an average rate of change?
G001 — The proposed permitted endpoint inputs are x0=0 and x1=0. Is their difference a valid nonzero denominator for an average rate of change?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-rate-denominator-validity, denominator_validity]
After
derived = [distinct_endpoint_eligibility]
Conditions: none
Use the declared scalar/set/Yes-No/fraction answer role;integer fractions retain/1.Do not add an undeclared domain or change original bilingual data,formulas or questions.
Rule: R56_source_answer_role_and_EXACT_family_interface · Uses: G001
Before
Rate ORIGINAL x1 minus x0 := sub(0, 0)
After
Rate ORIGINAL x1 minus x0 = 0
Conditions: none
Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
source roles = [0, 0, 0]
After
derived = [No, No]
Conditions: none
The average rate requires x1-x0 nonzero.Equal endpoints are a legal No eligibility case;do not compute0/0 or repair the endpoints.
Rule: Rate_equal_endpoints_legal_eligibility_NO_division · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.S002 · premise_and_result_audit — Recompute Rate ORIGINAL x1 minus x0 with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.No
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: f9753bd843f30963f62bf4fee1c2b5051c7a126078613e547976b6e723fc5da2candidate record SHA-256: a8dc64921e79cec866e54497564a072c745c83a0988c67ae9e7eb564f1788e40semantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759fLean: NOT_RUN · human review: NOT_PERFORMED