provably

the algorithm is provably optimal for this specific problem.

it's provably faster than the previous iteration by a significant margin.

researchers have provably demonstrated the existence of the new particle.

the system is provably secure against common hacking techniques.

the new route is provably shorter, saving time and resources.

this approach is provably more reliable in harsh conditions.

the code is provably free of critical vulnerabilities after testing.

it is provably beneficial to the company's overall performance.

the theorem is provably true based on established axioms.

the design is provably scalable to handle increasing user demands.

the result can be provably reproduced by following the precise steps.