What I'm getting at is I'd like to know how the Monero network can know that a key image used in a transaction is not either forged (probably an easy answer) or created from a different output owned by the same wallet (perhaps a more technical, but hopefully straightforward, answer).

The transaction private key, x, probably signs the ring and the key image, right? My hunch is that the distinctive ring signature provides a way to check the math that P (the output public key) being spent is a ring member, and is also associated with I, the key image that's attached to the ring signature.

How does it work? I don't understand how the verification works without revealing the actual tx pub key being spent.

I've been reading other SE questions and answers here, here, and here. I haven't found an answer expressed in the way I'd like to understand it.