user135718: I am aware that the identity on elliptic curves is the infinity element.
Long shot (as it would be very useful to me): with that being said, does there exist a public key, pk, on secp256k1 such that, combine(pk, x) = x for all x?
combine is via (https://github.com/bitcoin-core/secp256k1/blob/cd470333351bd6d90296352f2a957f38bbdaf014/src/secp256k1.c#L725)

user208: As you pointed out, the identity is the point at infinity. It is also the only identity for addition over the elliptic curve.
But infinity is not a valid public key, for a number of reasons, and thus also not a valid input to combine.

135718: <p>I am aware that the identity on elliptic curves is the infinity element.</p>
<p>Long shot (as it would be very useful to me): with that being said, does there exist a public key, <code>pk</code>, on secp256k1 such that, <code>combine(pk, x) = x for all x</code>?</p>
<p><code>combine</code> is via (<a href="https://github.com/bitcoin-core/secp256k1/blob/cd470333351bd6d90296352f2a957f38bbdaf014/src/secp256k1.c#L725" rel="nofollow noreferrer">https://github.com/bitcoin-core/secp256k1/blob/cd470333351bd6d90296352f2a957f38bbdaf014/src/secp256k1.c#L725</a>)</p>
 208: <p>As you pointed out, the identity is the point at infinity. It is also the only identity for addition over the elliptic curve.</p>
<p>But infinity is not a valid public key, for a number of reasons, and thus also not a valid input to combine.</p>
