[AnonymousXipang]

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.

[suspended_state]

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?

[AnonymousXipang]

“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.