In all of these chained proof protocols, the leader of slot n must include proofs of previous parts of the ledger. The designation of labor is specified in each proposal, e.g leader of slot n includes a proof of the transactions in slot n-k. This coupling of proof production with block production coordinates everything. L1 state updates require further action and therefore a separate protocol. There are several possible avenues here (e.g slots, races), all mostly orthogonal to proof production.
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