Foreign learners are often taught that Russian verbs always come in aspectual pairs, with the perfective verb formed from the imperfective verb either by changing the stem or adding a prefix. The two verbs are supposed to be synonymous in every way, except that one is perfective and the other is imperfective. If the perfective verb is formed from the imperfective verb by adding a prefix, the fact that the two are synonymous means that the prefix must be "semantically empty", i.e. have no meaning or effect on the meaning of the word, and just denote that the verb is perfective.
Question: Do such verbs actually exist? In other words, are there perfective verbs formed by adding a prefix to an imperfective verb, for which the prefix does not mean anything?
One example that is commonly given is писать and написать. However, some authors argue that even in these cases the prefix isn't actually semantically neutral, but that it "overlaps" with the meaning of the original imperfective verb in such a way that it de facto doesn't affect the meaning. A monograph detailing this hypothesis can be found here or here.
So ideally an answer to this question would in part address the answerer's opinion about the validity of the "overlap hypothesis". I.e. whether it makes more sense as a learner to focus on "aspectual pairs" as opposed to more general "aspectual clusters" (for which there might not be a one-to-one correspondence between imperfective and perfective verbs).
Background: (totally unnecessary to read, unless you're really curious)
Thinking about this question was motivated by this answer to another question.
That answer mentions biaspectual verbs, which challenge to some extent the idea of Russian verbs as always belong to aspectual pairs. On the other hand, most research shows that the majority of biaspectual verbs are foreign borrowings, so the argument could be made that most simply have not been present in the language long enough to develop full aspectual characteristics.
However, what seems to me even more problematic to the aspectual partner model are imperfective verbs which don't have a single "all-encompassing" perfective partner. Instead there exist multiple perfective versions, each formed by adding a different prefix, and with a different meaning. I have asked at least two questions already on this site about these verbs, here (курить) and here (смеяться), which also motivates in large part this question.
Such verbs can be interpreted somewhat so as to rectify the aspectual partner model, namely by interpreting the imperfective verb as actually being biaspectual, and forming imperfectivizations from each of its various hyponymous perfectivizations, and interpreting each resulting imperfective/perfective pair as a derived aspectual pairs. However, as with the examples of посмеиваться and засмеиваться, this interpretation seems somewhat forced, since the imperfectivizations are often rarely to never used or don't have the same original meaning as the perfective verbs they were supposed to be derived from. See also this question.
The linguist Janda writes, for example here, that Russian verbs are more naturally interpreted as belonging to "aspectual clusters" than "aspectual partnerships", in contradiction to the grammar usually taught to foreign learners.
The biggest seeming counterexample to such an idea are those imperfective verbs who, unlike the examples of курить and смеяться mentioned above, form perfective verbs using so-called "empty prefixes", i.e. prefixes devoid of any semantic content, but just signal that the verb is to have the perfective aspect instead of the imperfective aspect. For example, писать and написать. Such examples seem to also be the greatest motivation behind the "aspectual pair" model usually taught to foreign learners, since the model works most neatly and cleanly for such verbs.
In order to explain this, Janda and others have advanced the "overlap hypothesis", which claims that most, if not all, of so-called "empty prefixes" for perfectivizing verbs actually do have semantic content -- it is just that the semantic content of the prefix "overlaps" with the meaning of the original imperfective verb in such a way that it does not restrict the meaning of the resulting perfective verb, i.e. leads to a synonymous rather than hyponymous verb, despite not being semantically void/empty. They have written about this in a monograph explained in detail here, with some explanation of the methodology found here. Other sources explaining the hypothesis: (1)(2)(3).