1) Deliberately 2) Incontrovertibly 3) Obviously 4) Provably 1) Incontrovertibly 2) Provably 
• (adv.) In a demonstrable manner; incontrovertibly; clearly.
De·mon'stra·bly adverb In a demonstrable manner; incontrovertibly; clearly. « Cases that demonstrably concerned the public cause.» Clarendon. 
[adv] - in an obvious and provable manner
demonstrably 1. In an obvious and provable manner. 2. Capable of being demonstrated or proven. 3. Clearly evident, or obvious: 'They had a demonstrable lack of concern for the general welfare of their country.'
provably adverb in an obvious and provable manner; `his documentary sources are demonstrably wrong`