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Rollups are a Layer 2 scaling solution designed to enhance the scalability and efficiency of blockchain networks. In short: rollups are blockchains that rely on another layer-one blockchain (especially Ethereum) for settlement, while providing better scalability and performance guarantees compared to the underlying blockchain. Here’s a breakdown:

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Bundling Transactions

Rollups work by aggregating or “rolling up” multiple transactions into a singular transaction or a batch. This process occurs on a separate Layer 2 blockchain, which is a secondary framework built atop the primary (Layer 1) blockchain​.

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Off-chain Execution

The execution of transactions is performed off-chain in rollups, thereby reducing the data that needs to be posted to the main blockchain. This is particularly beneficial in congested blockchain networks where the high volume of transactions can lead to slower processing times and higher fees.

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Posting to Layer 1

Once the transactions have been bundled and executed off-chain, a single transaction or a summary of the batch is posted to the main (Layer 1) blockchain. This action retains the security features of the primary blockchain while significantly reducing the data load, as only the rolled-up transaction is recorded on-chain​.

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Optimistic Rollups

You can deploy Arbitrum Nitro and OP Stack rollups via Caldera — both of these stacks are “Optimistic” rollups. The term “optimistic” in Optimistic Rollups comes from the optimistic assumption that transactions within a rollup are valid. In the “happy path” where the rollup is acting honestly, no on-chain proof of correctness is required. However, if the rollup sequencer acts maliciously or errantly, a “fault proof” can be submitted to the L1 and prevent incorrect execution from occuring.
Want to learn more about Optimistic Rollups? View this article from ethereum.org

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Zero-Knowledge Rollups

You can deploy ZK Stack and Polygon CDK rollups via Caldera as well — both of these stacks are “Zero-Knowledge” (aka ZK) rollups. In contrast to optimistic rollups, ZK rollup nodes must submit a validity proof for verification to update state. The validity proof is a cryptographic assurance that the state-change proposed by the rollup is really the result of executing the given batch of transactions. This means that ZK-rollups only need to provide validity proofs to finalize transactions on Ethereum instead of posting all transaction data on-chain like optimistic rollups.
To learn more about ZK Rollups, view this article from ethereum.org