I am writing a paper aimed at a physics journal which extends an old paper (not by me), which introduced a mathematical formalism for a physical problem in a rather handwaving way and without addressing most of its mathematical background. In addition to exentding this formalism, my paper elaborates on this mathematical background and relatedly introduces the formalism in a ”more rigorous” way. I consider the latter one of my paper’s key features for the following reasons:
- One might consider the formalism and the methods derived from it not to be properly substantiated in the old paper.
- Though the mathematical background has no other application so far, it is interesting for its own sake and perhaps from a philosophical point of view.
- My approach to the formalism might be more accessible to some people and make them give a better understanding of what they are doing when applying the formalism and related methods.
As these points are rather opinion-based, I do not intend to elaborate on them in the paper – at most I might shortly mention the didactical aspects in the conclusion. (I mainly mentioned them here to give you some idea what I am talking about.) However, I do want to briefly mention in the abstract or the introduction that I “rigorified” the formalism, where briefly can be anything between one word and two sentences. For example, my abstract could look like:
[Old paper] introduced [old concept], which is useful for [application]. We extend this concept to [new concept] and also rigorify its mathematical background.
My problem is that rigorify its mathematical background is far from what I actually want to say. I am therefore looking for a way to say this without seeming arrogant or condescending on the old paper and in particular without implying that the old paper “did not do its mathematics properly”.
I intentionally do not give my best solutions for now, as I do not want to induce any bias on them, in case I may underestimate them.
I am also torn between Academia and English Language & Usage for posting this question.