In the subordinate clause that follows the verb guarantee, it uses the present indicative mood rather than the present subjunctive mood to state a fact. If you say, "I require that this be done immediately," then it is an order, not a fact, and it becomes the present subjunctive.

Guarantee just says that it will happen no matter what. The verb does not show any importance and does not carry out any orders. Merriam-Webster's Dictionary agrees with me and has this sentence:

They guarantee that the diamonds [that] they sell are top quality.

Sources

1. https://www.merriam-webster.com/dictionary/guarantee

To guarantee that does not require a subjunctive verb. A subjunctive seems to be just one of several possible constructions used in this context.

For clarification, I will first present my definition of "subjunctive," a term that can be associated with some confusion. In this context, the only thing I will call "subjunctive" is a finite verb with the same form as the infinitive, such as "that it be..." in your examples. The "subjunctive" does not encompass constructions like "that it should be..." that make use of auxilary words like should that do not have infinitives and that can never show any distinction between indicative and "subjunctive" forms.

So, I would say that a subordinate that-clause following the verb to guarantee is definitely not required to have a subjunctive verb: it is indisputably correct to use a modal auxiliary (such as will, shall, 'll, would, should, won't, wouldn't, shouldn't) followed by an infinitive instead. In many circumstances, the construction with a modal auxiliary is probably not only a possible option, but also the best option (as John Lawler says in a comment).

Unfortunately, I have not been able to find any "official" sources that tak about whether an indicative or subjunctive finite verb is appropriate after to guarantee that.

My personal intuition as a reasonably well-educated native speaker of American English is that there is nothing wrong with using the indicative in this context. The subjunctive, on the other hand, sounds strange to me (and judging from the comments, to some other people as well). And British English speakers supposedly have even less tolerance for subjunctives than American English speakers in general.

Since I don't have any official sources, I decided to look for examples in United States Supreme Court opinions (using FindLaw's search tool) since these are generally quite formal documents and they may provide some indication of how the verb "guarantee that" is usually used in formal writing.

The results of my search reinforced that the modal auxilary + infinitive construction is more common than either an indicative or subjunctive verb in that-clauses after the verb to guarantee. However, I was able to find examples of both subjunctive and indicative finite verbs being used in this environment.

One of the documents I found used both the "guarantee that" + subjunctive and "guarantee that" + indicative constructions in different places, which could either indicate interchangeability of the two constructions for the author, or the observance of some kind of distinction.

Dictionary evidence

"guarantee that" + subject + modal verb + infinitive is well-attested in dictionary examples

As I said earlier, this construction consists of a modal auxiliary such as will, shall, 'll, would, should, won't, wouldn't, shouldn't followed by an infinitive. Since dictionaries are commonly thought of as resources that describe standard usage, you may be convinced that it is standard to use a modal verb in the clause following to guarantee that by the following examples from dictionaries:

• I guarantee that you'll like this book.

(American Heritage Dictionary)

• The management guaranteed that outsourcing wouldn't mean job losses.

• I can guarantee that you will enjoy the film.

(Cambridge Advanced Learner’s Dictionary)

"guarantee that" + subject + indicative verb is attested in at least the Merriam Webster dictionary

The indicative "simple present" form is certainly commonly used in this context (as the question indicates). Unfortunately, there seem to be fewer examples in dictionaries of this type than there are of the modal verb + infinitive type, but I did find an example in Merriam-Webster:

• They wanted a guarantee that the document was authentic.

(Merriam-Webster)

I think that would be good enough for most people, although really serious prescriptive peevers might find Merriam-Webster to be too "permissive" to be a reliable source of information about grammar and other aspects of "proper" English:

I do not recommend the nation’s bestselling dictionary, Merriam-Webster’s Collegiate, tenth (1993) or eleventh (2003) editions, for several reasons. The print is uncomfortably dense, the writing is stiff, and the Collegiate is the most permissive of the major American dictionaries. It sanctions many questionable, eccentric, and stigmatized pronunciations, and its usage notes often take great pains to justify locutions that many authorities find objectionable and that are best avoided.

(Charles Harrington Elster, a self-identified "language maven")

"guarantee that" + subject + subjunctive doesn't seem to be documented in the dictionaries that I checked

I might have missed something, but I didn't find any example sentences in dictionaries showing the use of a subjunctive verb in this context. Of course, this is not an indication that the dictionary-makers find this usage illegitimate; they might just be unaware of it or think it's too rare to mention.

Supreme Court evidence

There were so many examples of the modal verb construction in the Supreme Court documents I looked at that I didn't bother recording any of them.

I found an example of the use of the indicative after to guarantee in Potter Stewart's majority opinion for Gannett Company, Inc. v. DePasquale (1979):

In Faretta v. California, 422 U.S. 806 , by contrast, the Court held that the Sixth and Fourteenth Amendments guarantee that an accused has a right to proceed without counsel in a criminal case when he voluntarily and intelligently elects to do so.

But I also found an example of the use of the subjunctive after to guarantee in Justice Blackmun's concurrence to the judgment of Morris v. Slappy (1983):

Properly understood, however, the interest recognized by the Court of Appeals does find [461 U.S. 1, 20] support in other cases and does not require any court to guarantee that a defendant develop a rapport with his attorney.

Interestingly, this document shows more examples of the construction "guarantee that ... will develop..."; I don't know if the use of the subjunctive instead of will + infinitive in this particular sentence has any significance. Perhaps the "not require" earlier on can somehow affect the verb form used in clause at the end of the sentence.

Even more confusingly, I found use of both the subjunctive and the indicative after to guarantee in the following Supreme Court document: Riley v. National Federation of Blind, (1988), opinion of the court delivered by Justice Brennan.

• North Carolina cannot meaningfully distinguish its statute from those previously held invalid on the ground that it has a motivating interest, not present in the prior cases, to ensure that the maximum amount of funds reach the charity, or to guarantee that the fee charged charities is not unreasonable.

• Consequently, what remains is the more particularized interest in guaranteeing that the fundraiser's fee be "reasonable" in the sense that it not be fraudulent.

There doesn't seem to be any absolute rule for this case, but I personally feel that 'guarantee' works better with the indicative form, as in "the parents should guarantee that their child stays out of trouble" simply because to guarantee something seems implicitly indicative; or else how could it be guaranteed? In short, the construction could not afford to offer any element of doubt!

Consider which sounds right: "Can you guarantee that your child pass this test?" or "can you guarantee that your child WILL PASS this test?" I find the indicative form much more appropriate here. I also found that if we take many examples of 'guarantee that', the subjunctive does suit certain cases, yes, but feels quite awkward in many others, whereas the indicative never feels awkward in any case! I think whoever uses the subjunctive with 'guarantee that' is probably using the form either in a specialised setting (as in quoting rules or laws, for example) or else imitating the structure of 'ask that' or 'require that' which of course DO use the subjunctive.

Similar ambiguity can be encountered with phrases like 'demand that' and 'make sure that' ('the teacher demanded that he get/ should get his spelling right' -- 'the teacher asked him to make sure that he get/ gets/ got his spelling right) where the final choice is often made depending on the context; so I feel there is no 'absolute right' or 'absolute wrong' usage in this type of situation.

Moreover, American English is quite liberal and has its own stylistic traditions, such as dropping words like 'that' which are considered technically necessary in British English, so (that) 'guarantee' even works without 'that', as in "can you guarantee your child passes this test?" -- such flexible grammatical conventions probably allow BOTH FORMS of the usage in question to be correct, in context.

Both sentences mean a different thing. Similar to how “suggest” with the indicative mood is suggestion of fact, and “suggest” with the subjunctive mood is a form of advice.

With the indicative mood, “guarantee” makes a statement of fact, such as:

I personally guarantee you that our entire staff is excellent.

However, with the subjunctive mood, it creates a causative claim, such as:

Our rigorous selection process guarantees that our entire staff remain excellent.

Of your two example sentences, I would personally read the first as:

x must stay finite, in order for it to ensure that the above representation stay meaningful.

And the second as:

x must stay finite, in order for us to be able to claim that the above representation stays meaningful.