Final Summary
Negative public key values exist mathematically, but they are abstracted away in Bitcoin's implementation. This abstraction leads to the common misconception that public keys cannot be negative.
I am not assuming that a coordinate has no positive or negative values in the intermediate process, but that it does not indicate an order relationship between public and private keys. Both are simply two possible points on the curve of a coordinate, i.e. there is no relationship in this regard to their order. If there were a way to identify them, it would not be through this.