"SkullCoin" runs on and is secured by the bitcoin blockchain which is proof-of-work and a crypto-currency.

This is true, but this is a separate proof-of-work mining from what you are proposing as a proof-of-work mining. The hash collisions being computed by the BTC network certainly do constitute proofs. This has nothing to do with the context at hand, however.

The "SkullCoin" folding@home mining pool provides all the information you need to keep track of payouts and be sure that you are getting what you deserve. This is a proof-of-work system.

This might be where you are confused. A proof, in the formal sense used in the notion of "proof of work," must be able to be independently verified as satisfied. One wishing to confirm the validity of the proof must be able to re-trace all of the steps from the assumptions made to the conclusion drawn. If one cannot resolve an assertion stack for it, it is not a proof. If one cannot construct an SMT solver for it, it is not a proof.

To say that one proof of work system is better than another is your opinion and has no substantiating proof behind any claims.

I am not saying that one proof of work system is better than another. I am saying that what you have been calling a proof of work system is not a proof of work system. Whether or not a proof holds is not a matter of opinion, either the proof holds and is factual or else the proof was not a proof to begin with. Further, once a proof is shown to hold then either no external influence can change it's validity or else it was never really true that the proof held to begin with.

The problem is that you've taken proof-of-work and removed some of the initial assumptions/axioms by re-centralizing an authority on verification!

I'll give you an example. Let's hypothesize that the Stanford servers get hit by a meteor tomorrow. Does the "proof" offered over the work done still hold, then? Can it be independently validated?

There is an unreasonably large set of (fatal) assumptions that get re-introduced into the "proof" when you put the onus of authentication back onto a single entity like this.

What if hackers and griefers control the team stats just like they controlled your Roblox servers?

What if the operator of those Stanford servers, or even some night staff kid in the data-center NOC, sees an opportunity for "free money" and just changes some numbers in their database to make fake work?

What if someone just hacks you and your networks and fakes the team stats for you so you see different numbers from the rest of the world, and send out coins based on incorrect data? Then you'd have an intended proof which does not hold prima facie but coins already distributed based upon it! (Something that cannot ever happen with a coin base claim in a correct proof-of-work implementation.) Similarly, what if you just make a mistake (you're only human) and fat finger in an additional zero or two on a distribution? The subsidy relation breaks down in a heartbeat and again the intended proof falls over at the axioms.

You cannot have a proof that starts with "So assume that this large set of random people on the internet are honest and also assume that this large set of routers and servers have not been compromised and then assume this manual process goes correctly every single time." Your QED quickly become intractable.

It seams to me that you are stuck on doing things only one way and anyone who tries something different is wrong.

Yes, I am "stuck" on not calling something that cannot be independently validated as satisfying it's constraints a proof. Silly me, wanting things claimed as facts to be evidently factual, particularly when they define a seigniorage on a currency I might use.

To say that this is not a crpto coin and that I may be lying and am confused is all "FUD" and not worth responding or refuting.

If so, then why respond and refute it? If your proof really did stand on it's own as a proof, I'd agree that you'd have to do little but laugh at me and point to the QED.

This is where I start to worry whether you are really so confused or if the lady dost protest too much.

I am afraid that the uncertainty of the nature of your proofs is creating doubt. I assure you I am no troll or "FUD"der. I think anyone who knows my posts would attest.

You can believe anything you want just have proof when bringing up assumption's if you want to be taken seriously.

Yay irony!