You can't do anything useful with checkpoints due to the same-site origin problem. Unless you can get browser support for some sort of proof of work that did something useful that whole line is a non-starter. No single origin involves a useful amount of work.
The problem is that this problem is going to be all overhead. If you sit down and calmly work out the real numbers, trying to distribute computations to a whole bunch of consumer-grade devices, where you can probably only use one core for maybe two seconds at a time a few times an hour, you end up with it being cheaper to just run the computation yourself. My home gaming PC gets 16 CPU-hours per hour, or 56700 CPU-seconds. (Maybe less if you want to deduct a hyperthreading penalty but it doesn't change the numbers that much.) Call it 15,000 people needing to run 3-ish of these 2-second computations, plus coordination costs, plus serving whatever data goes with the computation, plus infrastructure for tracking all that and presumably serving, plus if you're doing something non-trivial a quite non-trivial portion of that "2 seconds" I'm shaving off for doing work will be wasted setting it up and then throwing it away. The math just doesn't work very well. Flat-out malware trying to do this on the web never really worked out all that well, adding the constraint of doing it politely and in such small pieces doesn't work.
And that's ignoring things like you need to be able to prove-the-work for very small chunks. Basically not a practically solvable problem, barring a real stroke of genius somewhere.
The problem is that this problem is going to be all overhead. If you sit down and calmly work out the real numbers, trying to distribute computations to a whole bunch of consumer-grade devices, where you can probably only use one core for maybe two seconds at a time a few times an hour, you end up with it being cheaper to just run the computation yourself. My home gaming PC gets 16 CPU-hours per hour, or 56700 CPU-seconds. (Maybe less if you want to deduct a hyperthreading penalty but it doesn't change the numbers that much.) Call it 15,000 people needing to run 3-ish of these 2-second computations, plus coordination costs, plus serving whatever data goes with the computation, plus infrastructure for tracking all that and presumably serving, plus if you're doing something non-trivial a quite non-trivial portion of that "2 seconds" I'm shaving off for doing work will be wasted setting it up and then throwing it away. The math just doesn't work very well. Flat-out malware trying to do this on the web never really worked out all that well, adding the constraint of doing it politely and in such small pieces doesn't work.
And that's ignoring things like you need to be able to prove-the-work for very small chunks. Basically not a practically solvable problem, barring a real stroke of genius somewhere.