No, my friend. The digital signature used in Bitcoin transactions is not available for everyone to see, and it is not stored in every Bitcoin wallet.

When a user signs a Bitcoin transaction with their digital signature, the signature is included in the transaction data, but it is hashed and encoded using a cryptographic algorithm before being broadcast to the Bitcoin network. This ensures that the digital signature remains secure and private, and it cannot be easily read or deciphered by anyone who intercepts the transaction.

However, the public key, which is derived from the digital signature, is generally available for everyone to see, and it is used to verify the signature when the transaction is broadcast to the network. This is why Bitcoin wallets typically display public keys alongside Bitcoin addresses, as they are used to receive funds.

In addition, while digital signatures are not stored in every Bitcoin wallet, most modern wallets include a built-in mechanism for securely signing transactions using your private key, ensuring that your transactions are authorized with a valid digital signature before being broadcast to the network.

Overall, while digital signatures are a critical component of Bitcoin transactions, they are kept secure and private, and they are not generally available for everyone to see or store in every wallet.