Is Zakat a cost on wealth, or is it expenditure and allocation?

Zakat (definition): An obligatory right on specific wealth, for a specific group, at a specific time. It is defined as giving a portion of the annual nisab (definition) (threshold) to a poor person or similar individual, who is neither a Hashimi nor a Muttalibi. It has a pillar, which is sincerity (ikhlas (definition)), and a condition, which is owning the annual nisab. And it has conditions for the one upon whom it is obligatory, which are sanity, maturity, and freedom. It has a ruling, which is the dropping of the obligation in this world and the attainment of reward in the Hereafter, and a wisdom, which is purification from impurities and elevation of status.