When do changes make a manuscript a new paper?

Question

Suppose one submits a paper to a journal which gets rejected for reasons unrelated to correctness.

Say the paper can be though of as having 2 parts: A and B. If one eliminates part A and adds a new part C, and re-structures part B significantly, is it a "new submission?"

So it is really a question: when does A+B not equal B''+C? Assume that the original plainly stated B as the goal and the new paper plainly states C as the goal.

My specific field is math (probability theory, stochastic processes), but I think the question might be answered similarly for any field.

My specific situation is that the editors declined to send the paper for review apparently due to style and uncertainty about if the paper has anything (sufficiently) novel (probably again hard to recognize due to "style"). Comments were effectively: "it seems correct, but I don't know what is novel here, and I don't understand what these parts mean."

For me, part B was really the goal and part A was necessary to establish it. I found a way to eliminate part A, and I added part C (which was truly my original goal, but just made the original paper way too long). Also part B is now going to look significantly different and more efficient.

I know that a careful editor might notice that there are some parts that did appear in a previous submission (depending on how carefully they read the original), but should obviously notice the new parts. And I know that it is risky to resubmit to the same journal, even with significant changes, especially for an author with low prestige/status.

Answer 1

"Difference" is obviously a continuous variable (continuous in the practical common-language sense) and "otherness" is an emerging property. In other words, "otherness" is inherently fuzzy and no exact definition can be given. A legal system would take refuge in the opinion of an archetypical, well-meaning expert in the field.

Now, in your case, let me take the role of the legal system expert and state that there is clearly enough difference between the two submissions to make them different.

In a practical sense: (1) Make sure someone else has read your paper to make sure that it is understandable and that the introduction explains what is new. This advice is not so obvious. As authors, we are (almost) all selectively blind and readability is not something we are good at evaluating in our own papers. I am directing this advice just as much to me as to you.

(2) Consider laying out the case to the editor, starting with a Mea Culpa and explaining why this is a different submission. This would depend on what the editor exactly said. Editors are working in the field and might or might not be willing to forgive someone for submitting an unnecessarily difficult to read paper depending on whether they remember that they also were foolish on occasion.