We look for the High Quality Accreditation of tertiary education in two ways: one, involving large amount of information, including issues such as self-assessment, high quality, statistics, indicators, surveys, and field work (process engineering), during several periods of time; and the second, in relation to the information contained there about High Quality, which involves the development of an intelligent architecture based on both knowledge and models towards competitiveness. Mathematical and computational models for dynamic and structural analysis of the academic governability integrate the engine for this architecture. We specially consider that the processes of High Quality Accreditation demand a great effort, with the participation of numerous people and faculty members, and the compliance with government regulations. Architecture makes it easy to walkthrough top down and bottom up: from macro to micro level of data (and vice versa), covering the whole processes of the university, in order to verify the full compliance with the accreditation rules, policy and quality assurance of the entire academic programs. These architectures allow us to follow up the progressive enhancement in search of the academic excellence.