Proof of work vs proof of stake
How proof of work and proof of stake secure a blockchain differently, what each costs, and why only proof-of-work coins can be mined.
Two ways to agree
Every blockchain needs a way to decide whose version of history is real without a central authority. The two dominant answers are proof of work and proof of stake. They secure the chain very differently, and only one of them involves mining.
Proof of work
In proof of work, producing a block requires real computation, and the chain trusts the history with the most work behind it. Rewriting the past would mean redoing all that work, which is prohibitively expensive. This is what miners do: spend computing power to earn the right to add blocks and collect the reward.
Proof of stake
In proof of stake, there is no mining. Participants lock up (stake) coins for the right to propose and validate blocks, and misbehaviour can cost them their stake. It uses far less energy, but security rests on locked capital rather than expended work, and you need coins to take part rather than hardware.
Where Pearl fits
Pearl is a proof-of-work coin, which is why you can mine it with a GPU. Its twist is Proof of Useful Work: the computation that secures the chain is real matrix maths rather than a throwaway hash, so the energy does something useful while still providing proof-of-work security.