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I have a spending validator that currently expects an output with an NFT to be recreated at its own address. Is it necessary to also include a check whether the output's value has a greater equal ADA balance of minAdaTxOut (minAdaTxOut Reference)

Or is this done by the 2 phase node validation process?

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In theory no; In practice maybe.

If min ada is not present in each output then the Tx will fail regardless of validator.

But. Min ada as implemented in Plutus is hardcoded to 2 ada. This is not how min ada works. Min ada is calculated against the size (of data) of the utxo. More than three NFTs? that'll be more than 2 Ada required in the same utxo.

If your using constraints then you'll need to bear this in mind, since these details may really matter https://github.com/input-output-hk/plutus-apps/blob/c4cc9ee1add8f421e57789befb6a0c90621801f1/plutus-ledger-constraints/src/Ledger/Constraints/OnChain.hs#L123

How to calculate min ada is a bit convoluted. Why isnt a function in plutus-apps for it? No idea. Why wasn't it implemented properly... ?

You can extract the logic from here https://docs.cardano.org/native-tokens/minimum-ada-value-requirement/

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