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Let's first define a valid Bitcoin private key as a number in the range of [1, 115792089237316195423570985008687907852837564279074904382605163141518161494336], and a valid Bitcoin public key as a public key derived from a valid Bitcoin private key.
Then my question is: Is there a way to determine whether a specific point on the secp256k1 curve is a valid Bitcoin public key?
The secp256k1 curve has cofactor one, so every point on the curve can be written as a multiple of the generator. As a result, there are exactly as many points on the curve (excluding the point at infinity) as there are valid (nonzero) private keys.
In short: yes, every point on the curve is a valid public key.
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