Declared evidence_mode=complete_finite_list, certificate_parameter=19. 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=19. 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.
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.