Only the finite prefix values=[11, 12, 11, 13] is given; no infinite continuation is specified. Give (prefix, whole_sequence_boundedness_certified, infinite_subsequence_certified, convergence_certified, boundary).
G001 — Only the finite prefix values=[11, 12, 11, 13] is given; no infinite continuation is specified. Give (prefix, whole_sequence_boundedness_certified, infinite_subsequence_certified, convergence_certified, boundary).
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 historical interface marker while listing ordered output fields without JavaScript.Fields and tags are not extra mathematical evidence;fixed No markers retain their claim scope.
ORIGINAL finite prefix only=[11, 12, 11, 13];NO infinite law specified
After
whole_sequence_boundedness_certified=No;infinite_subsequence_certified=No;convergence_certified=No;these are missing certificates,NOT claims every continuation is unbounded/divergent
Conditions: none
A finite prefix can admit bounded or unbounded extensions.Without a whole sequence law,a finite cluster search supplies neither an infinite index map nor an all-later convergence certificate.The three No markers do not classify unknown continuations.
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
Result
([11, 12, 11, 13], No, No, No, finite_prefix_cannot_certify_whole_sequence_boundedness_or_infinite_convergent_subsequence)
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.