Proof of Stake with cold wallet

Could it be possible to prove you hold the ADA that you do hold if it is in a cold wallet? I’m just wondering how we could achieve a proof of stake while having our ADA in a wallet rhat isn’t plugged into the internet.

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I think the concept of a “Wallet” is going to confuse the general public.

Your ADA, to the extent it actually exists, is located in the network nodes. They don’t know whether the owner of the coins is online at any given point in time.