Doesn't it carry over from initial ledger balances starting from back when eth was proof of work?

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thats possible if nodes still validate the pow chain. but this would mean the security diminishes as the pos chain grows longer

i mean. this is not really the case.

its not necessary that the past chain is vulnerable to do a double spend attack. you can rewrite the chain after accepted transaction.

all you need is enough fake blocks for someone to accept transaction as complete. 10 blocks? 30 blocks?