After revision of the primary and secondary characteristics I have come to the conclusion that State Art is the most vital characteristic. It is not only offers material culture for archeologists and anthropologists to study/showcase in museums, but it is also an indication of wealth within a state. This is true in ancient and modern terms. To expound, investing in State Art proves moderate success concerning primary needs (food, security, resources, stable environment). Moreover, art is a reflection of society. It responds, as well as challenges the community. I am not saying art catalysts agriculture or religion or state authority, but it is the best signal that these are factors have been strongly established.
Usually, the first artifacts archeologists find are creative in nature—ceramics, figurines, wall paintings. Why are they so easily discovered? Because they are prized possessions for individuals (oft interred with them in a mortuary context), meant for communication and aesthetic appeals to the senses/psyche. This outlook continues to modern day society; ancient artwork is why museums are so attractive to a populous. Whether it is cavemen paintings, delicately carved woodworks, or adorned headdresses, ornamental and stylistic accent can be ascertained. Furthermore, personal interest in artwork only comes after a certain point of comfort or well-being.
Wealth: artistic endeavors by the state mean an abundance of valuable possessions because it is usually an afterthought. Following the accumulation of scarce resource such as food, water, weapons to establish a stable state consisting of a sizable population, defined territory, sovereignty, and governing elite COULD the state indulge in creative expressions that offer zero marginal utility. Also, little to no labor allocation by the state (citizens can choose an occupation). When a state is powerful enough to no longer depend upon its population for labor (an excess of workers), citizen specialization begins. Thus, the rise of artisans is attributed to an unregulated labor economy. Another byproduct of specialization is payment for labor. This bring me to the influence of religion on artwork. The manifestation of deities lining walls of pyramids, statues in palaces, figurines shrined in households, is worth a price with specialization. The capitalization of religion, a product of skilled craftsmanship, also influences society. It makes religion available for the plebeians.
The development of state art, while not a primary characteristic of an ancient state, is the most important in my opinion because of it only originate AFTER other vital facets of the state. Therefore, whenever art is found, there is likely other evidence present indicating agriculture, infrastructure, economy, and religion.