Learn English – What does ‘over’ mean

The "over that of" is a comparison that could be replaced with "more than" or "better than". Even as native English speaker, I had to read this sentence multiple times to understand it because of how long it is. Stripping out technical details, I've reduced the sentence to get a much easier sentence to parse.

"[This technique] raises [something] by a factor of 2 to 10 times more than [something else]"

The ambiguity between "over" meaning "more than" and "over" meaning "during" can only arise where an adverbial of time is expected.

In a sentence like:

• It's been over a minute (since he left).

we expect a noun or adjective phrase or an adverb of place after "be":

• It's been a mess these days.
• It's been noisy lately.
• It's been there for a while.

Notice that adverbials of time can only come after the words or phrases in bold above. That means that "over a minute" in your sentence cannot be an adverbial of time, meaning "during a minute," but a noun phrase meaning "more than a minute."

In:

I lived there over five years.

although we expect an adverbial of time after "I lived there," I don't think "over" usually collocates with the verb "live" to mean "during." In this case, we'd use "for" (or no preposition):

I lived there for five years.

With other verbs, like "extend," we may need to use both prepositions to indicate duration + "more than":

• The war extended over thirty years (= during thirty years)
• The war extended for thirty years (= during thirty years)
• The war extended for over thirty years (= during more than thirty years)