Use the declared rational deviation-probability tail p_n=1/(n+3) on nonnegative integer indices where this value belongs to[0,1], starting no earlier than max(0,numerator-shift). The common probability space and infinite-process interpretation remain declared premises, not constructions inferred from finitely many numbers. Keep exact reduced rational outputs with positive denominators, omitting /1 for integers. Evaluate index n=16. Give (numerator,shift,n,deviation_probability).
G001 — Use the declared rational deviation-probability tail p_n=1/(n+3) on nonnegative integer indices where this value belongs to[0,1], starting no earlier than max(0,numerator-shift). The common probability space and infinite-process interpretation remain declared premises, not constructions inferred from finitely many numbers. Keep exact reduced rational outputs with positive denominators, omitting /1 for integers. Evaluate index n=16. Give (numerator,shift,n,deviation_probability).
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.
nonnegative valid probability indices start at=0;only there0<profile<=1
Conditions: none
A positive denominator and value≤1 require n+s≥c.Keep the original index;do not clip values above1 or silently shift them.This checks arithmetic domain only.The infinite-process/common-space interpretation remains declared,and the prefix-only family gains no infinite continuation premise.
S003 · premise_and_result_audit — Recompute deviation probability at original index with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute deviation denominator at original index with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
Result
(1, 3, 16, 1/19)
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.