Declared evidence_mode=complete_finite_list, certificate_parameter=1. The registered modes complete_finite_list and universal_affine_injection refer to their supplied complete or universal certificates; failed_candidate_encoding records only a failed witness. Give (evidence_mode,certificate_parameter,proved?,classification).
G001 — Declared evidence_mode=complete_finite_list, certificate_parameter=1. The registered modes complete_finite_list and universal_affine_injection refer to their supplied complete or universal certificates; failed_candidate_encoding records only a failed witness. Give (evidence_mode,certificate_parameter,proved?,classification).
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.
qualifying declared certificate flag=Yes;classification=at_most_countable
Conditions: none
This audits the declared complete or universal certificate mode;the numeric parameter does not construct or verify an unspecified set.A failed encoding refutes that witness,not countability itself.At most countable does not mean countably infinite.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
Result
(complete_finite_list, 1, Yes, at_most_countable)
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.