Originate, arise, emerge - these are possible translations of the Slovak "vzniknúť" (others are spring, stem, issue, proceed and result from). The origin of something is the source (zdroj) or the cause (príčina) of its existence, so the focus of "to originate" is how something comes into existence. To arise contains the idea of growing upwards and getting bigger, but something abstract rather than physical (that is just "rise"), such as "cooperation" or "conflict".

To emerge means something more like "to appear slowly out of the darkness or fog, or out of a hole" (also "to issue from"), like an opinion that forms in a cloud of French Cartesian thinking. To spring is like water coming out of the ground, and to stem is like a plant growing up from its roots. To proceed is to continue step by step, and the result ("výsledok") means the opposite end of a process from the origin. To me, an author is someone who writes a text, usually fictional, so I prefer to translate "autor projektu" as the originator.