Good question Sam.
My understanding of corporate finance is that when a company issues shares in their company, they should be executed and recorded by an officer and the secretary of the company. The secretary has to keep a log of numbered stock certificate(s) of whom purchased shares and how many were purchased for each transaction(s).
After they produce the certificates of how many shares were issued to said individual(s) / corporation(s), they also have to keep traceability of those certificates numbers and number of shares when produced for sale. The repurchased certificates have to be cancelled and recorded. All for auditing transparency.
Today most shares are digital, but one can still request from the company a physical certificate. Usually for a fee. The digital certificates still have to be audited!
I am also under the impression that when a company "stock repurchase" takes place, the company has to cancel those shares sold. So the float and total shares will be reduced by taking them off the books. The company cannot reissue the same numbered stock certificate to another transaction. A company cannot keep two sets of books!
Naturally, all is in my opinions only.
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