I am writing about the analysis of a certain mathematical object. The expression for this object is obtainable in several ways:
- non-rigorous ways: they amount to just computations
- rigorous ways: they are precise and apart from the above computations, one needs to supply some proof of certain passages
I have a fully rigorous proof of the derivation of the expression for this object. I think that including it in my article is no good service for the community, because:
- there is no more space
- the proof is technical and not enlightening (no new ideas, essentially)
The only element of novelty is that the object is related to a new problem, not found in the literature, but very similar to others. And in a somewhat different formal setting than most other examples, but again, the proof outline and the key formulas/conceptual passages, are already present.
I am targeting a respectable journal where usually, facts are proved rigorously, not formally. And where proofs (formal or not) are not deferred to the supplemental material. That is the space for pictures, code description, implementation details and so on.
Should I include the lengthy proof, hence, in the supplemental material? How about including a non-rigorous proof using a quicker method in the appendix?
Otherwise, is it a good way to go just citing the various computation recipes out there, without spelling the computation (nor a proof) out in detail?
More about "The object"
I am working in optimal control and I have to compute a derivative of a functional. A non-rigorous proof would be to form a Lagrangian and differentiate it formally, without checking that things are actually differentiable, for instance (it is a bit more complicated but this is the essence). The Lagrangian approach is non-rigorous. For a fully rigorous approach one should prove differentiability of every piece and this takes considerably more effort. Say, using the implicit function theorem in function spaces.
The non-rigorous passages are especially already present in the literature, for examples more or less.similar to mine. The rigorous passages maybe are not exactly equal to something seen before, but there are standardized recipes to obtain them (e.g. apply the implicit function theorem).