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AES is not provably secure, for the simple reason that there is no security proof for it. We suspect that AES is secure in practice, but there is no proof of that.
I think you meant brute force when you mention, it would take trillions(?) years to break AES. So your "provably secure" category boils downs to brute forcing the algorithm which is not considered "breaking" the algorithm. AES is kind of a successor to DES (at least for an initial understanding) which had been in use for quite a long time and was not broken ...
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