Nut for binding post on AR 3A

Price mentioned was for Imperial steel nuts...5/32 x 32 tpi
97 Rupees per 100, and normal 25% discount on that (list) price..

32 tpi is 0.794 mm pitch, standard M4 is 0.7 mm, and the thread shapes are different.
Apart from the major and minor diameters being different of course.

We are bilingual here for fasteners, I just got 6 kilos of 3/16" x 3/4" hex head plated bolts.
About $2 a kilo, average 340 pieces per kilo.

Perfectly normal, and we still use BSP threads for pipe.
 
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Left field suggestion:
Spray the threads with silicone release, and put a clump of JB Weld like stiff epoxy, let it set.
Voila!
The mold release will not let the adhesive stick to the stud, and the end result will be nuts.
Or just buy the taps, and make them out of M3.5 nuts, drill and tap.
 
I did not expect them to fit.
Just get ordinary 5/32 nuts, and washers, they cost pennies here.

Rayma: I once sent 1/16" steel balls to someone in SF, he was not able to get 1.6 mm in the USA, and those were for the detents in a Japanese camera lens.
I talked to a friend who actually does more engineering work than me (I am into plastics), and he said 1/16" is 1.59 mm, close enough.
So I taped a few to a piece of paper, and sent it by post, which went missing.
The second letter made it, and he was able to use the lens once again.
The steel balls were like 20 cents for 144 in those days, the shop keeper did not even ask for money, for the 10 - odd I took from him.

Like I said, we are bilingual here, even bearings are sold in Metric and Imperial sizes.
 
#8 is an American series, roughly same as 5/32" in UK series.
32 is the pitch, 32 threads per inch, tpi in short form.
Some fasteners, even Metric, have standard (preferred) pitch, and non-standard (but in a standard series) pitch, sometimes with a particular use in mind.
You can look it up. I am at work, but there are different pitches for #8 nut, 24 and 36 IIRC.
So you must specify both, as in Metric.
5/32" is about the diameter you measured, 4.17 mm on the crest of the threads.
 
5/32" stove bolt is NOT the same as #8-32. 1/8" & 3/16" stove bolts were common in the 1950's but the numbered machine screws drove them off the market. Machine screws had better cut threads & didn't bind under power driver application as stove bolts could. The last car I saw with stove bolts was a 1934 Ford. My 59 fords were all machine screws, USS & SAE threads. Illinois Tool Works (ITW) and Rockford dominated sales to the auto & appliance industries for decades. I don't know if they invented the numbered machine screws.
The #8 screws in my stock can are .159" OD. The nuts are .147" ID. That is using an uncalibrated but new Fowler dial indicator. 25.4 mm/inch. 32 stands for 32 threads per inch. I don't have any brass #8 nuts.
 
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https://www.americanfastener.com/nuts/
It is a UNC thread, not BS...more used in automobiles than otherwise.

My first suggestion, change to Metric, was a quick and permanent solution I think. 4 mm is close enough, and can be done in a couple of hours.
Oddly enough, his stud measures 4.2, and your converted measurements are (screw)(0.159") is 4.03 mm, the nut (0.147") is 3.74 mm.
The OD for a 5/32" screw is 4.17 mm, closer to the 4.2 measured by the OP.
It is quite possible the speaker screws have been changed in the past, as they are quite old, and he got them a week or so back.
So we have to see the physical evidence rather than the theoretical evidence...
 
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This should be the pitch (as advised by a friend)

1644577032201.png
 
32 tpi is 0.794 mm, close enough.

The thread gauge is metric, there are similar sets for Imperial.
Metric threads are 60 degree angle, Imperial BSW are 55 degrees, UNC and UNF may be different threads in angle, major and minor diameter, in fact 60 degrees.

I would have finished the replacement with M4 x 0.7 by now...