1. Committee on National Security Systems (CNSS). (2015). Instruction No. 4009, National Information Assurance (IA) Glossary.
This document provides the verbatim definition used in the question. On page 10, "Certification" is defined as: "A comprehensive assessment of the management, operational, and technical security controls in an information system, made in support of security accreditation, to determine the extent to which the controls are implemented correctly, operating as intended, and producing the desired outcome with respect to meeting the security requirements for the system."
2. National Institute of Standards and Technology (NIST). (2010). Special Publication 800-37, Revision 1, Guide for Applying the Risk Management Framework to Federal Information Systems: A Security Life Cycle Approach.
In Appendix G, Glossary, page G-2, this foundational document provides the same official definition for "Certification," linking it directly to the accreditation process.
3. National Institute of Standards and Technology (NIST). (2018). Special Publication 800-37, Revision 2, Risk Management Framework for Information Systems and Organizations: A System Life Cycle Approach for Security and Privacy.
While modern RMF terminology has replaced "Certification" with the "Assess" step, the function is identical. Section 2.3, "The RMF Steps," describes the Assess step as the process to "determine if the controls selected for the system...are implemented correctly, operating as intended, and producing the desired outcome." This aligns perfectly with the classic definition of certification.