Since it seems not a lot of the top replies actually read the paper and just seem to have read the title and dismissed it, I've summarized some of the fraud claims in the paper below.
The paper is NOT just claiming that regular shorts are stock manipulation. It outlines a series of tactics and loopholes in detail that involve the use of shorts among other market tools to sell people stocks that don't exist, but were counterfeited through book-keeping tricks.
Their claims of counterfeiting stock involve the use of naked shorts(a.k.a where a share is sold, but never borrowed) Naked shorts must be attached to a real share within 3 - 21 days, not doing so is illegal. They outline a series of loopholes which are used to sell shorts w/o ever borrowing a real share, effectively diluting the actual stock issued by the company with extra counterfeits to drive the price down. The goal is to drive the price to 0 and bankrupt the company, so that the shorts don't have to be covered anymore, netting a large (tax-free) profit.
Below is not an exhaustive list of manipulation tactics, just a selection of examples:
1. SEC rules left a loophole allowing naked shorts to be covered with naked calls. No actual instance of stock has to actually be borrowed in this case, but it's not marked as a fail-to-deliver in SEC reporting. The naked call option is not tied to any stock issued by the company, it's just an option to buy at a future date, but it can now be repeatedly borrowed out for shorts as if it were a stock.
2. The SEC keeps track of fail-to-deliver in the SHO list and has requirements of 3 days for brokers and 21 days for market makers to borrow an actual stock. Another fraud claim is that brokers/hedge funds collude to pass around naked shorts between offshore shell companies in order to indefinitely reset the 3 day SEC requirement to keep naked shorts indefinitely and keep it off of the SECs fail-to-deliver list. They also use a similar technique to allow 8 - 10 shorts to borrow the same shares and then just move them around in time to meet SEC reporting deadlines. During any audit by the SEC, the SEC calls ahead and they move all naked shorts to offshore accounts where they can't be seen and then move them back once the investigation is over.
This means for every fail-to-deliver marked on the SECs books, there will be several times (10 - 20 according to the whitepaper) more counterfeit shares being sold by shorts that are not tied to any real shares.
3. The third fraud claim involves the clearing house (a.k.a a broker for brokers) the DTCC (we care about two of its subsidiaries DTC and NSCC). When a broker sells a short and fails to deliver an actual share in 3 days, before 1981 they would be forced to buy it back. After 1981, they can borrow one from the NSCC Stock borrow program. The NSCC will then go to the DTC which holds all the stock certificates and find a broker with a surplus of shares and borrow the necessary amount of shares.
Now here's the fraudulent part. When the shares are borrowed only the net amount is deducted from the surplus, but no actual shares are actually removed from the individual accounts of the broker. Now both the lending broker and the borrowing broker have real shares in their account, but they're the same real shares. Since the borrowing broker has real shares now, these same shares can again be lent out by NSCC to another borrowing broker and again no shares are removed. Now 3 investors have the same shares in their account. Since transactions are done as net transactions (instead of individual stocks) between brokers, the fact that 3 investors have the same share never has to be reconciled and two counterfeit shares have been created.
In regards to the GME short, even though only 71 million shares were issued by the company, currently institutions have reported to the SEC (13F filings https://fintel.io/so/us/gme) that they own more than 113 million shares (including 13% owned by gamestop ceo).
Additionally according to the SEC's fails-to-deliver list for December, Gamestop has nearly 1.8 million shares failed-to-deliver. Most companies have anywhere from 0 to a few thousand. Going by the whitepapers estimates the number of counterfeit shares would be 10-20 times that amount, indicating that ~ 40 million shares of Gamestop would be counterfeit.
In order to verify these accusations with concrete data, we would need access to the books/transactions of the DTCC. They are a private organization that is collectively owned by brokers and they are very secretive and have few disclosure requirements due to regulatory capture at the SEC.