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The documentation says:

Stellar requires accounts to hold a minimum balance of 1 XLM before they actually exist. Until it gets a bit of funding, your keypair doesn’t warrant space on the ledger.

How long does the end user have to send funds and create their account? What could happen if I provide a public key to an end user and he takes a long time to fund and create his account?

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Short answer: the keypair never expires.

Since the public key is essentially a computational result of so called one-way function, the public key can be derived from the secret key itself. Therefore, the term "keypair" refers to a pair of a secret key and complementary public key that can be regenerated from a secret key. The keypair is generated offline (or at least without touching Stellar network), so the network doesn't know anything about your new keypair until you send a transaction containing CREATE_ACCOUNT operation for the public key of this keypair.

When the account is created, Stellar Core servers create a corresponding ledger entry which matches the public key of the keypair. After that we can say that the account exists on the ledger. You can even delete the account using MERGE_ACCOUNT op and recreate it later using the same keypair.

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