Learn English – “If anyone knows” or “Does anyone know”

I thought I'd add this as well, just for those who are inferring that "Here Be Dragons" is an inference on the illiteracy of the scholars during the middle ages. I've separated it out from the other answer because it's not a direct answer to the question.

Anyway, "Here Be Dragons" is actually just an example of Old English (it is invalid modern English)- in particular it's just an inversion of a sentence in the Old English sentence ordering.

In particular

Here Be Dragons

Is an inversion of

[if] here, there Dragons are

In much the same way that in Jack and the Beanstalk the sentence

Be he alive or be he dead, I'll grind his bones to make my bread

is an inversion of the sentence

[if he is] alive or dead, I'll grind his bones to make my bread

Now "If here, there dragons are" is a word ordering that is no longer valid (although the word order should be familiar to German speakers which has the same sentence structure as Old English), and that is why the sentence "Here Be Dragons" is no longer valid.

Note that the subjunctive form in English is still there, so we can construct our own sentences to show that this is still valid English so long as we shuffle the word order around:

I must insist that you be here by 9 am tomorrow for a debrief.

I agree with the recommendation that komodo dragons be here in the public part of the zoo where visitors can see them.

So anyway, long story short is that "Here Be Dragons" used to be valid English, but no longer is. Its use idiomatically is used to insinuate "oldness" rather than "illiteracy".

These are two sentences combined into one:

The Soviet Union is no more, but the entity created specifically to counter its military might thrives.

This is talking about the present. Said "entity created specifically to counter its military might" is still thriving at that point.

The Pentagon's budget increased relentlessly until 2011, topping $700 billion.

This talks about the past. The Pentagon's budget increased before this point. It does not, however, tell us if the Pentagon's budget is still thriving, so we can't use the present form "does" here. We could use "did":

The Soviet Union is no more, but the entity created specifically to counter its military might thrives.

As did the Pentagon's budget, which increased relentlessly until 2011, topping $700 billion.

The "As" here simply refers back to "thrives" and indicates, as above, that "the Pentagon's budget" thrived just like "the entity created …".

The Soviet Union is no more, but the entity created specifically to counter its military might thrives as did the Pentagon's budget, which increased relentlessly until 2011, topping $700 billion.

The choice between "has" and "did" here is mostly at the author's discretion. Personally, I would pick "has" instead of "did" because "did" implies the budget increased completely on its own, but as I said, both would be grammatically correct.