attempt to clarify double spending
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@ -745,7 +745,8 @@ $\widetilde{C} := S_K(C_p)$:
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only to the mint.
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\item The mint validates $\mathcal{D}$ and checks for double spending.
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If the coin has been involved in previous transactions, it sends an error
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If the coin has been involved in previous transactions and the new
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one would exceed its remaining value, it sends an error
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with the records from the previous transactions back to the merchant.
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%
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If double spending is not found, the mint commits $\langle \mathcal{D} \rangle$ to disk
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@ -1113,7 +1114,8 @@ an exclusive right to redeem deposit permissions for the coin for a
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limited duration. The merchant uses the lock permission to determine
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if the coin has already been spent and to ensure that it cannot be
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spent by another merchant for the {\em duration} of the lock as
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specified in the lock permission. If the coin has been spent or is
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specified in the lock permission. If the coin has insufficient funds
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because too much has been spent or is
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already locked, the mint provides the owner's deposit or locking
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request and signature to prove the attempted fraud by the customer.
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Otherwise, the mint locks the coin for the expected duration of the
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