Thanks! From the added context:
7. Pirrani's suit relied on Section 11 of the Securities Act. This alleges that the company lied in its registration document.
8. In an IPO, all shares are covered by the registration document. In a direct listing, the current shareholders of the company just start trading their shares on the market one day.
9. Notably, a direct listing makes it unclear which shares are registered (covered by the registration document) and which are unregistered. According to SCOTUS, Pirrani can't tell, so he can't prove standing under Section 11.
10. He should have sued the company under Section 10 of the Securities Act instead. This is the same mechanism used against "mature" companies. Lawyers don't like to sue under Section 10 because of reasons.
Some stuff which is still unclear to me:
1. People speak of owning n shares of a company. I always thought this was simply shorthand for something like: "I own shares #1034852, #1092647, and #2986246".
2. People sometimes own 0.25 shares of a company, but I thought that this was a convenience invented by stock brokers like Fidelity and Robinhood.
3. If each share is associated with a share number, and people only hold whole shares in principle, then isn't the provenance of that share clear? Whether it is registered or not should simply be a matter of following it back in time?