A better link for Cochran, Hardy and Harpending (2006) is this one here (not a draft): https://booksc.org/book/11348250/d2fa70 This one is final and has the proper page numbers, whereas for some reason that draft copy and another non-final version still lacking the final page numbers are easy to find.

Let's have a look at Levinson (1959) and Backman (1972) (for the 112-115 claim) and Lynn (2004) (for the 107.8 claim).

There is no 112-115 claim in Backman (1972). Rather, Backman (1972) as interpreted through Lynn (2004) makes a 107.8 claim. There is no mention of 107.8 whatsoever in Backman (1972), so Lynn seems to be making this calculation out of the provided tables. He was doubtful about the accuracy of these tables himself:

The Backman (1972) study provides IQs for several of the second order factors (given in the introduction to this paper) but these are so variable and in some instances so low as to raise doubts about their credibility.

These results are in need of checking and replication. At present it is doubtful whether any conclusion can be reached about the intelligence of American Jews except that their verbal intelligence or, if this is preferred, their gc (crystallized intelligence) is about 107.5.

A 107.8 figure is thus derived from Lynn looking at tables he thinks are likely inaccurate to begin with. Cochran, Hardy & Harpending (2006: 661) seem to have just taken the Backman (1972) study uncritically, and if Lynn's interpretation is correct, an article that posits a 107.8 IQ is simply an incorrect source for the 112-115 claim. Cochran et al do not include any reason for why they think Backman's result suggests 112-115 whereas Lynn at least proves he looked into it.

Your Levinson (1959) link appears to be broken, but it is easy to find a copy: https://booksc.org/book/173930/972924 Either way, it looks as though this claim must also be made from interpreting the provided table.

As for Lynn (2004), while the sample size certainly seems problematic, he may also have a dodgy conception of White, e.g. Jews are considered White and therefore he uses the term 'Gentile' for what we tend to mean by White (i.e. European people with very low levels of non-European admixture), and I have no idea whether he regards MENAs as 'Gentile' or 'Other'. He does place Asian and Hispanic in 'Other' at the very least. I am very skeptical that as late as 1990-96 one could manage to get a sample size that is 81.85% White, i.e. 5300 Whites out of 6475 total. Was America still 81.85% White on average in 1990-96 considering that it's below 50% underneath the age of 18 or so in 2021?

Lynn (2004) concludes with an interesting point I've somehow not yet considered, and the argument can be put somewhat like this using fairly normie assumptions:

1. Blacks are discriminated against
2. Black IQ is lower than White IQ
3. Jews are also discriminated against
4. Jewish IQ is 'higher' than White IQ
5. If we combine 1/2, lower black IQ than White IQ could be because of discrimination
6. But if we combine 3/4, Jewish IQ is not lower than White IQ despite discrimination
7. It does not make sense to claim that discrimination lowers the IQ only of one group being discriminated against, but not another group being discriminated against
8. Therefore, lower black IQ than White IQ cannot be the result of discrimination

I can think of two ways someone might try to avoid this conclusion, thereby keeping the argument essentially intact until more premises are added to break it again. Of course, these are normie premises—I obviously don't think 1/3 have held true for decades, I'm obviously disputing 4 or I wouldn't have made these comments.

I think the origins of '115' appear to be the high end of the estimates of Jewish verbal IQ in The Bell Curve (1994) as interpreted by Lynn (2004: 203) where a 107.5-115 figure is given. Perhaps this high end of Jewish verbal IQ is simply being misinterpreted as the average overall Jewish IQ. The Bell Curve does not appear to make any specific claim about Jewish IQ, and Lynn doesn't provide the page numbers for where he thinks this claim is located.

Even a Jewish average IQ of 107-108 (if we accept for a moment both the 107.5 figure in Lynn [2004] and the 107.8 figure in Backman [1972] as interpreted by Lynn who doubts the figure) seems at odds with the Israel 92 average IQ claim. Even if Israel is 20% Arab as RadicalCentrist claims, I doubt that's going to drag the figures down to 92 given that Arab average IQ is in the low-mid 80s.

Someone could do the math: If 80% of Israel has 108 IQ to be generous, and 20% of Israel has an IQ of 85 to be generous, there is no way that you end up with a 92 average as the answer. I've done this with 100 numbers (80 108's and 20 85's) and got an average of 103.4. Either the 92 average is too low or the Jewish/Arab averages too high. The discrepancy is obviously even more pronounced if we change those 108's into 115's.

Two other observations I've made:

Firstly, it's interesting that all three sources cited in Cochran et al come from people who are almost certain to be Jewish themselves. Levinson was at Yeshiva University, Manhatten.

Secondly, it's interesting that this 115 figure seems to rely heavily on people who the System hates, i.e. Richard Lynn and Charles Murray. It is unsurprising that these two are treated as acceptable sources when speaking of Jews but not when speaking of other non-whites except when making another System-friendly claim (East Asian > White in IQ). If you have any idea where the supposed East Asian IQ superiority claim originates from I'd also like to know. I know The Bell Curve is one source in which this claim is made.