Consciousness as a puzzle, the observer as a mirror, and AI's place in this circle

I am a long time hobbyist turning Cyberneticist. What that is, is an algorithm which partitions a finite length of binary into disjoint discrete limits cycles. Since the “product” of such as objects is more than simply a result of dynamics; I’m championing it’s usage as a mathematical object. Traditionally, I have read that, a limit cycle is typically an ending of some dynamics. Suggesting it as a proper mathematical object may be fringe however, there are valid arguments that defend the suggestion. So there is C code on github under ernst03 I am going to be learning until I die so I welcome feedback on my assumption. -Ernst