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How are each world's discoveries stored and managed?

Each world's shared discoveries are saved on the server in BepInEx\config\DiscoverySync\worlds\<world id>.json.

The same file lists each character under Characters, with a short Id, the character's name, the player's platform ID (such as a Steam ID) and a Status:

Discoveries maps each shared item to the Id of the character who discovered it first, for example "Wood": 1. 0 means Unknown.

"Characters": [
  { "Id": 1, "CharacterName": "Freki", "PlatformId": "76569453934611979", "Status": "Accepted" }
],
"Discoveries": {
  "Wood": 1,
  "Stone": 0
}