establishes
v.v. to start something that is meant to last for a long time, like a company, a system, or a rule. It can also mean to prove that something is true.
v. to set up an organisation, system, or set of rules on a firm or permanent basis; to achieve permanent acceptance or recognition for something. Often used to describe the act of proving a fact beyond doubt.
The new law establishes clear rules for online safety.
The university establishes a new scholarship fund every decade to support students from low-income backgrounds.
By publishing the results of the five-year study, the research team establishes a definitive link between sleep quality and long-term cognitive health.
The verb is transitive and requires a direct object. In formal writing, it often takes a 'that' clause when meaning 'to prove'.