provably
Adverb
Meaning
in an obvious and provable manner
Source: WordNetSynonyms
Antonyms
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his documentary sources are demonstrably wrong
Analysis Hilbert's paradox is a veridical paradox : it leads to a counter-intuitive result that is provably true.
Ball, p. 485 Since non-Euclidean geometry is provably relatively consistent with Euclidean geometry, the parallel postulate cannot be proved from the other postulates.
However the halting problem is provably undecidable and so such an algorithm does not exist.
For example, the system of primitive recursive arithmetic (PRA), which is widely accepted as an accurate formalization of finitistic mathematics, is provably consistent in PA.
It is not known whether these cryptographically based authentication methods are provably secure, since unanticipated mathematical developments may make them vulnerable to attack in future.