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Definition of Enshrined

• If a rollup chain posts its blocks and proofs to a settlement layer that acts as a settlement hub such as Ethereum, we say that the settlement layer is enshrined if the canonical chain and its transaction validity rules are determined by the settlement layer.

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Definition of Non-Enshrined

• On the other hand, if the rollup posts its blocks and proofs to a settlement layer but the canonical chain of the rollup is ultimately decided by the rollup network itself, we say that the settlement layer is non-enshrined. In order for a non-enshrined settlement layer to make sense, it should have a way to upgrade the rollup that does not require hard forking the settlement layer.

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Sources

• https://blog.celestia.org/sovereign-rollup-chains/#rollups-on-ethereum