What application? Your tree shows a common ancestor between chimps and man and the link is not even identified. It is a mysterious creature.
You don't need to be able to identify the common ancestor to infer its existance based on extant DNA samples.
Why not unicorns and munchkins?
Humans and chimps demonstrably exist and have DNA that we can study.
It would appear they do not even know what it was. There is a number substitute instead of a name. The majority of your chart is littered with numbers as opposed to actual names which appear on the right.
A number can be a name like any other.
Would it make you feel better if we just called it "Joe"?
Stars have numbers assigned to them as well, does that mean those stars also don't exist?
You guys don't even know what they are? A host of theoretical and undescribed creatures.
Suppose the parents of X and Y died in a fire and all evidence of them disappeared.
Would it then be "theoretical" to infer based on the DNA of X and Y, that they shared a common ancestor whose identity is unknown?
It's not "undescribed" either. Knowing what a human is and what a chimp is, we can certainly make relevant predictions concerning the traits that common ancestor most likely had. These predictions are also what enables us to recognise it, if it would show up in the fossil record.
Your case is weak. It is unconvincing based mostly on faith.
If your case is based mostly on "faith", then I certainly agree that it is very weak.
Evolution though, being a well-established theory of biology, is anything but faith based...
Like all well-established scientific theories, it is based on very solid evidence. And
lots of it.
Fictions are incompatible with science which is a search for truth.
Indeed. Which is why more sophisticated people get their info about the world from 21st century scientific investigation, instead of bronze-age books.
Your tree is a visual of a myth, nothing more
That tree isn't conceptual. It's a representation of very real, independently verifiable, data points from the real world.
If not then make your case for a common ancestor.
The tree is the case.
That you don't (want to) comprehend how this tree is obtained, is the problem.