How two Cauldron2D.Worlds, one on each machine, play one game with rollback: each runs the game on its own clock, applies its own players' input at once, and runs frames again when the other's input arrives late.

Every join, leave and input is an action stamped with the frame it applies before. A world stamps its own players' input delay frames ahead of the frame it is on, and sends it to its peer once. The host also stamps every join and leave, its own and those the other world asks for. Each message also says up to which frame the sender has sent every action of its own (through) and which frame it is on.

A frame is run with the actions known for it. A player whose input for a frame is not yet known keeps their last input, so held buttons stay held and none is pressed or let go. When an action arrives for a frame already run, the world loads the state it kept from before that frame and runs the frames again. The game's events from frames run again are dropped. A world runs no further than window frames past its peer's through (advance?/1).

Each world measures how far ahead of its peer it runs: its frame less the peer's last reported frame, once for every frame it sends. Every 250 milliseconds it averages those and sends the average. When its own average less the peer's is 1.5 frames or more, it owes 0.3 of that many waits, at most window, and skips one step in every three until it has waited them (wait/1). The world behind never hurries.

Each world sends the checksum (Cauldron2D.Game.checksum/1) of the state before every 60th frame once both worlds have confirmed it. A checksum that differs is counted in desyncs and nothing else is done.

delay/2 picks the delay from the round trip between the two worlds, and delayed/2 changes it while the worlds play: input stamped further ahead leaves frames with no action, which keep the last input, and input stamped nearer comes after the actions already sent for its frame, in the same order on both worlds.