I'm pretty new to crypto and I'm confused about POW

POW Is usually explained like this...

1. A group of transactions are bundled into a memory pool (mempool).

2. Miners verify each transaction in the mempool is legitimate by solving a mathematical puzzle.

STOP!

How does solving the mathematical puzzle (finding the hash for the nonce) have anything to do with "verifying" the transactions? Isn't the the hashing puzzle just to keep miners from spamming the network? Thus, requiring work (and time to pass) to earn block rewards? Maybe I'm wrong here, or getting confused but isn't the verifying of transactions a function of signature verification with the public key? What does that have to do with the hashing puzzle??

When people say POW "secures" the network, what do they actually mean?

1. The first miner to solve the puzzle gets rewarded with newly minted bitcoin (the block reward) and network transaction fees.

2. The verified mempool, now called a block, is attached to the blockchain.

POW Is usually explained like this...

A group of transactions are bundled into a memory pool (mempool).

The usual terminology would be to say that: a group of transactions are selected from the mempool of the mining node, and they are bundled into a block.

Miners verify each transaction in the mempool is legitimate by solving a mathematical puzzle

In order for a transaction to be entered into the mempool in the first place, it must be a valid transaction. So the node will check the transaction to make sure it is valid according to the network's rules and current state.

How does solving the mathematical puzzle (finding the hash for the nonce) have anything to do with "verifying" the transactions?

It doesn't. Verifying/validating a transaction would generally refer to checking to ensure it is valid. Confirming a transaction would generally refer to it being included in a new valid block on the network.

When people say POW "secures" the network, what do they actually mean?

The energy spent hashing to try to find a new valid block is what secures the network. See this question for an explanation. The validation of individual transactions before they are included in a block template is not considered to be part of this.

The first miner to solve the puzzle gets rewarded with newly minted bitcoin (the block reward) and network transaction fees.

Yes, compensation for the security provided.

The verified mempool, now called a block, is attached to the blockchain.

Again, to nitpick terminology, the mempool is not turned into a block. Rather, transactions are selected from the mempool, to create a block candidate that is hashed, slightly altered, and hashed again, until a valid block construction is found. This valid block is then broadcast to the network, and will in most cases end up becoming a part of the blockchain history.

• Ok that makes sense. BTW, I'm literally ripping these bullet points verbatim from this article: hackernoon.com/…
– GN.
Apr 1, 2021 at 20:51
• @GN. doing a quick skim of that article, I would say it is somewhat poorly informed / outright wrong on many points. Apr 1, 2021 at 21:36