Synonym of "High-Level" in "High-Level Ideas/Description/Method"

Question

I'm writing a paper and we have the following quote.

see Section 1.3.4 for a high-level description of the method and Section 2.1 for the specific application.

Basically, we're using a general method which we outline in Section 1.3.4; in Section 2.1 we describe our application of this method. As a native English speaker, this sentence seems fine to me. However, someone who is French 1 suggested that we change it with the following comment.

for a high-level description of the method », maybe replace « high-level » by some other adjective, such as « precise ». (Feels more modest.)

We certainly are not intending to be arrogant! Rather we are describing the ideas at an abstract level.
So my question is two-fold.

(a) Do people agree that this may come off as arrogant (not modest)?
(b) What synonyms for "high level" are there? 2

1 : but at least fluent enough in English to be at a university in Austria in a department which uses English as its main language.
2 : other than perhaps "abstract" (but not sure it means exactly the same thing...) I am struggling to think of any; a well-known internet search engine has not been as helpful as one might expect

Jason Bassford · Accepted Answer

It seems to me that high-level description is somewhat redundant. I know it's possible to have a detailed description, but if description is used on its own, without qualification, I would assume it would be high-level anyway.
From Merriam-Webster's definition of description:

1 b : a statement or account giving the characteristics of someone or something : a descriptive statement or account
       // The review was little more than a description of the film's plot.

As such, I see nothing wrong with just the following:

a description of the method

However, if some kind of qualification is required, you could used general rather than high-level:

[Merriam-Webster]
6 : relating to, determined by, or concerned with main elements rather than limited details
    // bearing a general resemblance to the original

Using general is more understandable than high-level, which might not necessarily be easily understood by everyone:

a general description of the method

To provide contrast to general description, add what was mentioned in the definition of general as contrasting with it:

See Section 1.3.4 for a general description of the method and Section 2.1 for details of the specific application.

Synonym of "High-Level" in "High-Level Ideas/Description/Method"

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