I absolutely love your post Omega. I wasn't considering some of those points when I was typing up my analysis, and I'm really glad that you took the time to write up your counter-analysis. I think the rest of my theories stand pretty well, but yours here looks to be untouchable. Great stuff!

Again, I hope to remind you all that neither the Covenant, Flood, or Monitors refer to either Halos as Alpha or Delta. They must, therefore, be human designations. And, I remind you again that, in math, delta can mean the next in a sequence or a change. As in, Alpha was the first (obviously) and Delta was the next or different Halo. They are not being named one digit ahead. Delta is the fourth Greek letter and designates Installion 05, but Alpha is the first and designates 04. In this case, Installation 04 is called Alpha because it was the first one we saw. Installation 05 is Delta because it's the next one we saw. Get it?

Oddly, I can't find any Internets references to the "next in a sequence" thing so I'm probably wrong on that, but I could have sworn I've seen it defined as that before. But I also don't remember Bungie saying that they haven't said who named the Halos and extra-Halo objects. If indeed it wasn't the humans, I wonder who it could have been. But if there is some sort of complicated naming scheme vs First = 04, Different = 05, I'd go with the latter. It's simple and makes sense, and we don't have enough evidence for the former. Looking at it purely scientifically, I mean.

I do not think the installations are in alphabetical order for the reason that the moniter's numbers would be out of order.

1
1x7=7
7x7=49
49x7=343 (Guilty Spark - Alpha Halo)
343x7=2401 (Penitant Tangent - Delta Halo)
2401x7=16807
16807x7=117649