Ok. Then define race scientifically within genetics. Not a fringe paper, a pet theory. Provide the established scientific definition of race as it is understood in genetics.

You have it backwards. No wonder you're confused. Race is the caucasian race, and within it we have the english race, the scottish race, and so on. It is based on divergent/common ancestry and you can zoom out or in as you please.
We then see if genetics correspond to and agree with our understanding of race, and wouldn't you know? It perfectly does. We aren't imposing a structure onto the genetics to make it fit our understanding of race. We aren't creating a definition based on our knowledge of genetics. In fact, the strength of the concept of race is that it came BEFORE genetics but even then, genetics confirm our concept. This is the strength. This is called scientific. No overfitting, no ad-hoc changes based on empiri, etc. Simply does the 'model fit the new data' and yes it does.

If we are doing science, we MUST presume objective measurements.

Not how science works. Any measurement is based on presumptions and earlier hypothesises. You might consider something "objective" but it is only within your paradigm.

I just know from many of these debates that yall always try to move the conversation away from science and to philosophy or HISTORY, as you do here.

No. I did not invoke history. I invoked the scientific understanding of race before our universities in the west were taken over by marxists after ww2.
"historical concepts in science known as human races"
If you have problems with reading comprehension, then try to re-read paragraphs to increase your comprehension.

If you haven't noticed, I don't subscribe to your "scientific" (political) priests or so-called authorities or "consensus". I adhere to actual science. If you want to debunk the concept of race, then don't change the definition or the concept, and then debunk that. This is a strawman and entirely semantic. Instead work with the definition and understanding that scientists used before your "priests" changed the definitions.

Of COURSE clusters match historical partitions because HUMANS SET THE K VALUE. They intentionally male the clusters resemble historical categories. This happens in 100% of all machine learning cluster operations for race.

This simply shows that you do not even understand what an unsupervised algorithm is or how machine learning works. Why do you think I said unsupervised instead of using the word supervised algorithm? It is specifically to avoid what you are postulating here, but you fail to understand the distinction- likely because this is not your field of expertise.
To make it easy for you to understand: we aren't intentionally making the clusters resemble historical categories. Literally the opposite. If you continue to fail to see the distinction here, then please let me know, and I may spend some time to elaborate on the basics of machine learning.
There is in fact ZERO reasons why the clusters should or ought to or would resemble the historical clusters IF race was not a thing. But because race is a real thing, then the clusters do resemble historical categories. Please take some time to consider these two sentences thoroughly.
Your confusion might also come from a lack of ability to understand conditional dependencies. Have you ever taken any courses in conditional probability?

There really is no substitute for cracking open a modern genetics textbook.

Appeal to authority. I don't adhere to your religion or your priests.

Your problem is that our human genetics perfectly match the historical categories, and your only arguments so far have been appeal to authority, consensus, semantics, and worst of all: complete lack of understanding of the basic algorithms used in the field of genetics. I'm looking forward to you coming with any scientific arguments.