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A 1... address encodes the hash of a public key (specifically RIPEMD160(SHA256(key))
). Since cryptographic hashes aren't easily invertible, the address alone cannot be used to convert between compressed and uncompressed keys. If however the owner of this address has spent coins belonging to it (or has otherwise published the public key), the public key is now known and can be used to construct an address from both its compressed and uncompressed version.
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