It’s not entirely a social construct, for example there are very clear genetic factors - you could use a clustering algorithm on genetic data to reveal there are very clear groups, regardless of which social culture is doing this clustering, the clusters would still emerge, because math.
You’re right that the borders are not well defined though - it is a probably distribution - just like the weights in a neural network are also a probability distribution
There are no clear genetic factors at all. They don't exist, because there are no clear biological delineations between 'races'. It's a purely social construct.
You maybe could sort of define a group of people coming from the same locality and having the same history , and they would have maybe some degree of biological similarity as well, but there would be a high number of those groups and even then it would be quite useless and with number of exceptions.
Set the bar at impossible so you cant be proved wrong. No system anywhere is 100% accurate, and to demand that as a standard only shows your numerical illiteracy.
Why is it impossible? It's certainly possible to tell apart cat and dog DNA. If the race theory proponents argument hold water, the same must be possible for different races.
Here is a link to the Kahn Academy course on statistics: https://www.khanacademy.org/math/statistics-probability
If you take this course, you will understand probability better, and then you wont commit the logical fallacy of "false dichotemy" where you try to reduce complexity to binary classes which is a view that is too simplistic to accuratly represent the distributions we are talking about
That image does not contain 'race', and it comes from a paper that does not even mention the word 'race'. You have provided no arguments that race exists. The paper writes:
> This observation ... will make it a challenge to trace the ancestry of African Americans to specific ethnic groups in Africa, unless considerably more markers are used.
The more markers you use, the more different groups you get. You can of course choose to 'cluster' them, but then some precision will be lost, and what exactly will be gained?
You’re right that the borders are not well defined though - it is a probably distribution - just like the weights in a neural network are also a probability distribution