Sure, put the file on Mega and anybody that wants to confirm can download the file and make sure that the hash checks.
I'm talking about a
cryptographic proof. Your suggestion doesn't correspond to the definition of "cryptographic proof".
Look, having cryptographic proof that there were 1000 accounts doesn't mean anything if you can't prove that those 1000 different accounts weren't sock puppets.
If you go and open your next play project for anybody and everybody, you will still get accused of only having 20 real people, each with 5-100 socks each. Why? Because cryptographic proof doesn't solve the sock puppet problem at all.
You are about to make the exact same mistake.
Cryptographic proof is really nice in combination with some other method of verification on sock-puppet identity. At least NEM finger-printed computers that registered tokens and weeded out lots of suck puppets. Your not doing anything even close to that.
You could go to a big Bitcoin conference. You could have little business cards and each one has instructions on how to set up a NXT account and an account on MS, and each card has a unique token or ID on it. You can pass out these cards to real people at the conference. For each card you hand out, you accept one business card from the other person, on the back of the business card they gave you, you write the corresponding NXT MS instruction card ID number. Now you have cryptographic proof combined with proof of business card.
There are of course other ways. You could create a facebook page called JINN, you could accept likes and they must become your friend, you would make your friends list open to the public and you would try to look at each Facebook profile to see if it was a sockpuppet. There are varying different ways to do this. For instance if you have 500 out of your 1000 are accounts from Nigeria, then you can know they are sock puppets. There are much more complex methods of sock-puppet removal too via Facebook. You could set the requirements quite high for Facebook activity. Because again, that proved that people made those worked to make those accounts, and furthermore you can profile each account.
You could use the BTT method I suggested.
The point is cryptographic proof doesn't solve the real problem. The real reason you want a wide distribution is to say it was "fair" and not gamed by 20 or fewer whales. Just giving cryptographic proof via MS doesn't do much for you there. You open up your MS to the world to mine JINN and you will have 20 people with 90%. You might as well just ask people to send you a bitcoin for a share of the new project.
(Yes, of course this isn't for "JINN" but that was just an example)