What's the name of the cookie used by Convex Auth? | Convex Community | Page 1

I would like to know what name convex auth uses to keep track of session tokens. I like knowing how tools I use work so I can make modifications at any time. By logging into https://labs.convex.dev/auth-example, I noticed that login state works even when there are no cookies, and later found out that Convex auth uses localStorage by default unless when using @convex-dev/auth/nextjs. Anyways, I have something like the ff in localStorage:

{
  theme: "system",
  __convexAuthJWT_httpsadmiredsandpiper807convexcloud: "ey...some_JWT_stuff",
  __convexAuthRefreshToken_httpsadmiredsandpiper807convexcloud: "some_refresh_token"
}

1- Is there a documentation for the exact names used for the tokens similar to what Clerk has here: https://clerk.com/docs/deployments/clerk-cookies#strictly-necessary-application-cookies. It is always good to know about the magic done by the library, since I might want to read them and pass them around myself somewhere especially on the server. I know there are certain utilities for Next.js, but I still want to know. (Also, even though the chances of collision with my own set cookie/localstorage values is extremely low, it's not zero.) From the sample above, it's evident that the string is built from the cloud URL with some prefix.

2- Is there a documentation for how to verify such tokens manually similar to what clerk has here https://clerk.com/docs/backend-requests/handling/manual-jwt.

3- Are these names the same for localstorage and cookies (guess this can be answered by 1 above).

#What's the name of the cookie used by Convex Auth?