In the context of Peirce's existential graphs, is this one valid?
I am tempted to interpret this as "There exists a non P", but it feels wrong to leave it as is, even though I can't think of a reason why it would not be valid.
I know you can extend the Line of Identity, by the rule of iteration, to get:
which is the standard way to represent "There exists a non P", but is the first Graph good enough?
I see what you're trying to do: with the $P$ predicate inside a cut, it looks like you have created a 'non-$P$' predicate, and by attaching the line of identity to that, you say that there is an object that is a 'non-$P$'.
However, just like propositional logic, there really is no 'non-$P$' predicate that you create our of a $P$ predicate together with a $\neg$.
That is, in classical logic, you have a $P$ predicate that you can apply to an object ... and then you can negate that to say that it is not true that something has property $P$. Formally, you first create $P(x)$, and then you can get $\neg P(x)$. .... you don't first create $\neg P$, and then get $\neg P(x)$.
Same for Existential Graphs. If you have a $P$ predicate, then we fierst need to apply that to an object (i.e. attach a pine of identity to it), and then we can negate that ... i.e. the cut needs to be around all of the $P$ predicate with a line attached to it. So, the second figure in your post is grammmatical, and the first is not.