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I see the Cardano epoch nonce being used as a source of randomness. How can a non-technical person verify if the nonce used is actually legitimate? Is there a source where I can find the nonce for a specific epoch without running a node myself?

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The best way to verify whether or not something on-chain is legitimate is to run a node yourself, be that a transaction, nonce, SC, or whatever else. CNCLI is an excellent tool for use with the node, and can be used to calculate the epoch nonce.

That being said, there are of course other third party sources for (almost) all on-chain data, but a quick google search yields no such luck.

Perhaps Andrew can help us out? :)

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If not running node/Daedalus:
Project Koios provides epoch_params endpoint that you can easily view (even from referred docs link), you can fill the epoch you're requesting and click Try button).

Else:
If using CLI with node, you can also use command below to fetch epoch-nonce without any thirdparty tooling:

cardano-cli query protocol-state --mainnet | jq -r .csTickn.ticknStateEpochNonce.contents

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