on verification of a DID

Forgive my ignorance. How do I prove that the pair-wise relationship with
the DID did:btc1:298347982739 is true. How is the public key
1LGpGhGK8whX23ZNdxrgtjKrek9rP4xWER? I was trying to play with
https://github.com/WebOfTrustInfo/btcr-did-tools-js to understand this but
I had difficultly getting the bitcoin from the testnet to play with my
bitcoin wallet.

"Public keys are used for digital signatures, encryption and other
cryptographic operations, which in turn are the basis for purposes such as
authentication (see Section § 5.4 Authentication
<https://w3c.github.io/did-core/#authentication>) or establishing secure
communication with service endpoints
<https://w3c.github.io/did-core/#dfn-service-endpoints> (see Section § 5.6
Service Endpoints <https://w3c.github.io/did-core/#service-endpoints>). In
addition, public keys may play a role in authorization mechanisms of DID
<https://w3c.github.io/did-core/#dfn-decentralized-identifiers> CRUD
operations (see Section § 7.2 DID Operations
<https://w3c.github.io/did-core/#did-operations>), which can be defined by DID
method <https://w3c.github.io/did-core/#dfn-did-methods> specifications."

https://w3c.github.io/did-core/#bib-did-resolution

At: https://w3c-vc.github.io/playground/

Input:

{
  "@context": "https://schema.org/",
  "claim": {
    "id": "did:btc1:298347982739",
    "name": "Alice",
    "knows": {
      "id": "did:eth1:93753829747",
      "name": "Bob"
    }
  }
}

Bitcoin (ECDSA Koblitz) Private Key for Signing

L4mEi7eEdTNNFQEWaa7JhUKAbtHdVvByGAqvpJKC53mfiqunjBjw

Bitcoin (ECDSA Koblitz) Public Key for Verification

1LGpGhGK8whX23ZNdxrgtjKrek9rP4xWER

Output:

{