IQ differences by race in the US.
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The ideal way to do heritability studies is by looking at adopted twins. Basically, what they have found is that if you take a Japanese kid whose parents had an IQ of 107, and put them in a white family whose parents had an IQ of 100, the best guess of his adult IQ will be 107, not 100. (family conditions generally have zero predictive power on IQ - the non-heritable aspects of IQ seem to us to be 'random' [most likely developmental events in the womb, or singular, unique events in environment that are individualized and don't effect multiple individuals])
The results are replicable throughout decades and hated by 99% of social 'scientists'.
It is true that you can train for IQ tests, though the extent to which will differ (everyone can get on Mensa is likely untrue). The ideal is to be taking a test that has not been specifically trained for, which at a population level, is generally the case, but can make the individual score unreliable. That IQ is generally measuring something real and something useful is indicated by its high correlation with life outcomes AND brain size.
Twin studies are small and can't control for every possible factors that can affect the environment. For example, asians are type casted as smart in the west from a young age. It can then become a self fulfilling prophecy to do things to be seen as smart by the asian kids. That is another one of these social study "fact" actually.. Find me a study that put an Asian twin from birth in a broken down African village or equivalent.. that way, with such a strong environment difference, we'll see if he's still 107 compared to his other twin
That sounds like a "trust the science bro" moment. Did you personally do a wide review of the published material or did you take that from the Jordan P consensus crowd? Fact is, you can train for it, you agree to this yourself, this means that there's a huge flaw in the test's ability to control for non-hereditary factors. Doesn't matter how many twin studies you bring up, I can take a random person off the street and raise his IQ by at least 10 pts just by making him practice yet he won't be an once more intelligent. We also know that there are correlations between the ability to solve IQ questions and that of math problems. You can teach math to kids and they get higher IQ scores.
Brain size is not static and can change based on what you do. The same is true for life outcomes. IQ is good at telling you what we already know: smart people are smart. It doesn't tell you how they got smart.