Term for "lower numeric bound" - analogous to “capped”

What term should be used for describing limiting the lower range of a number?

We (often) use "capped" to refer to a limit on the upper value of a range.

What is the analogous term for limiting the lower end of the range?

More:

I want a past tense word that means "a hard lower limit has been placed (on something)".

In the same way that we might say "Your medical costs have been capped at $5000" (that's the most you will pay), I seek a word where I can say "Your medical costs have been XXXXed at $200" (that's the least you will pay).

Solution 1:

It's not euphonious, and moreover colloquial, but floored is used in this context. More standard, but with a mathematical flavor, is bounded below.

Solution 2:

The Engineers I work with refer to the noun as "the floor," or the "lower bound." I do not believe there is an analogous single word to "capped," but you can certainly say, if somewhat less euphoniously than otherwise desirable, "lower bounded," or "always exceeds," or if speaking to a mathematician "is bounded below by."

Solution 3:

There are many ways to say this, though I can't think of one which is exactly what you're asking for. Precisely what you use will depend a lot on your context and your audience.

You might say exceeds:

The projected average temperature definitely exceeds the average of the previous thirty years.

You could also say at least:

We estimate a production rate of at least 3 units per hour.

But in some contexts, simply saying has a lower bound sounds much better:

The function has a lower-bound of 2x.

You might also consider a minimum of or at (a) minimum:

You will need to pay a minimum of $200 for your medical costs.
Your medical costs will be $200 at a minimum.