A function that can be proven to be computable is called provably total. These functions are called Provably Secure Cryptographic Hash Functions. SWIFFT is an example of a provably secure cryptographic hash function. The converse is not true, as not every provably total function is primitive recursive. While all primitive recursive functions are provably total, the converse is not true. If there were one, then the halting set would be decidable, which is provably false. This has bearing on the design of provably unbreakable cryptographic algorithms. It's provably impossible to create an algorithm that can losslessly compress any data. In cryptography, SWIFFT is a collection of provably secure hash functions. There exists boosting algorithms that provably maximize the minimum margin (e.g. see ). This guarantee is not given by most other provably secure hash functions. By extension, any convergent infinite [must be provably infinite] series would work. Algorithms with provably good online performance (addressing the exploration issue) are known. This follows since parallel lines provably exist in absolute geometry. Support vector machines provably maximize the margin of the separating hyperplane.