How is a Bitcoin transaction verified?

Bitcoin transactions are verified through a process called "mining" and confirmed by nodes on the Bitcoin network. Here's how it works:

1. **Transaction Initiation**: A user initiates a Bitcoin transaction by creating a digital message that includes information about the sender, recipient, and amount of bitcoins being sent. This message is then broadcast to the Bitcoin network.

2. **Inclusion in a Block**: Transactions are collected by nodes on the network and grouped together into blocks. Miners, who are specialized nodes on the network, compete to solve a complex mathematical puzzle that involves hashing the block's data. The first miner to solve the puzzle creates a new block, which includes the verified transactions, and adds it to the blockchain.

3. **Proof of Work**: Solving the mathematical puzzle requires significant computational power, known as "proof of work." This ensures that miners invest resources (electricity and hardware) to secure the network and validate transactions. Once a miner finds a valid solution, they broadcast it to the network for verification.

4. **Consensus**: Other nodes on the network verify the validity of the new block by independently solving the puzzle themselves. If the majority of nodes agree that the block is valid, it is considered confirmed and added to the blockchain. This process ensures consensus and prevents double-spending of bitcoins.

5. **Confirmation**: Once a block is added to the blockchain, the transactions it contains are considered confirmed. The number of confirmations a transaction receives depends on the number of subsequent blocks added to the blockchain. As more blocks are added, the transaction becomes increasingly irreversible, providing greater security against double-spending.

6. **Transaction Finality**: After a transaction has been confirmed by several blocks, it is considered final and irreversible. The bitcoins are transferred from the sender's address to the recipient's address, and the transaction is recorded on the blockchain for permanent storage.

Overall, the verification of Bitcoin transactions relies on the decentralized consensus mechanism of the network, where miners compete to add blocks to the blockchain through proof of work. This process ensures the integrity and security of the Bitcoin network, allowing for trustless and censorship-resistant transactions.