This is not a proof or a claimed solution.

The manuscript attempts to point out that one syntactic assumption inside the standard P vs NP formulation may behave inconsistently when it is expanded structurally.

I would appreciate refutation, counterexamples, or clarification from those familiar with complexity theory or formal logic.

I'm not sure I understand this article, but the argument you present seems to be that when considering P and NP as relational objects, they don't have the same signature, thus cannot be compared, so the statement "P = NP" is meaningless?

“Not comparable” doesn’t necessarily mean “meaningless.” Focusing on the structure behind “=” can give a different view.

If you want to explore it further, a place more suited to longer, multi-angle discussion would probably work better than here.

You should probably have linked the whole work which is briefly referenced at the end of the article, and isn't yet indexed by search engines. I found it by myself:

https://zenodo.org/records/18107880