I'm glad you recognize what you're doing. This is why science is a disciplined methodology and demands evidence.
"The fossil record does not show this. It shows sudden appearance of species, with nothing in between the species."
That's simply not true. Creationists have been spouting that nonsense forever, and they'll probably never stop.
BTW, using terms like "mathematico-spatial images", which haven't been used in and don't relate to the discussion, don't really help you sound smarter. The best thing you could do is to quit making assertions about what a theory demands when you clearly don't understand it well enough to know. It's when you do that that you demonstrate your lack of knowledge.
The term is used in research. Look it up.