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The side with all the teeth not the nubs for free float barrel nuts
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You said that this is your first barrel installation? There is a learning curve to installing standard barrel nuts with delta/slip rings (believe it or not), it's not always as easy as Legos.
I had my issues with installing standard barrel nuts when I first started out too. The best move I ever made was ditching those all in one type tools, such as the DPMS/Smith Enterprise style wrenches. They have a very shallow engagement of the barrel nut teeth and make it very easy to slip off and cause damage to the barrel nut and delta ring. I ended up switching to the 3 pin GI barrel nut wrench and found that it was much easier to use, but the fact that it only has 3 pins puts a lot of stress on only three of the teeth on the barrel nut, and the teeth will start to bend when you get up into the mid to higher torque range.
I got to a point where I gave up working on the AR15 until I could find a better barrel wrench. I wanted something that would be similar to the GI wrench but had more pins, which resulted in me starting this still ongoing thread, started long long ago. >
Barrel wrench thread.
That thread led to a few different prototype wrenches, which resulted in two of them (one from Spike's Tactical and one from BRD Engineering) becoming available for a little while.
Long story short, 2UniqueLLC eventually came out with a couple similar wrenches to what I wanted and I'm much happier. >
Link. >
Link.
After that I focused on barreling jigs. >
Barreling jig thread.