Thank you mystis! I'm glad you find my point interesting and civilizations fascinating. I am familiar with some of Asimov's works (Foundation ofc), as for your question the answer is no, the members of the civilization need not declare to be a part of it. I'm building this theoretical framework solely for humans to use as a means to quantify and compare the few key distinctive indicators of prosperity/advancement of a civilization. It is probable that an advanced and different civilization would not even be able to comprehend the notions used to build this framework, or that they would a framework of their own. :)

Edit: The members need only be part of the organizational and development efforts, live in the arbitrary area, and share a cultural and way of life baseline/order