>"It's a fine definition for an abstract" It is not. An abstract is one of the most important parts in a paper and that's why authors tend to avoid writing def

>"It's a fine definition for an abstract" It is not. An abstract is one of the most important parts in a paper and that's why authors tend to avoid writing definitions on them but stating something like "A definition for X is given in the paper". It is meant to "describe" the paper rather than a summary or introduction of the subject in question. In any case, writing a good abstract is hard, and it doesn't diminish the quality of this paper.