Introduction[]
Let's see if the World Rings qualify for Conceptual Manipulation on a Type 1 level
Definition[]
Looking at the Conceptual Manipulation page, a Type 1 or Independent Universal Concept, is defined as:
"1. Independent Universal Concepts: Such concepts are completely independent from the part of reality they govern, except maybe of other concepts of this nature. These concepts shape all of reality within their area of influence and at whatever level that area exists in, and everything in it "participates" in these concepts. For example, a circular object is circular because it is "participating" in the concept of "circle-ness". In this way, the alteration of these concepts will change every object of the concept across all of their area of influence, while the opposite wouldn't affect the concept."
So let's evaluate the Rings to see if they abide by this definition
Explanation[]
"completely independent from the part of reality they govern"
It is already accepted that the World Rings embody distinct emotions, but it would also be plausible that they are emotions themselves as on multiple occasions, such as when Sonic interacts with the Water Blue World Ring, an whirlpool of emotion begins to spiral inside of him[1]. The Rings' independence from the Arabian Nights was displayed in 2 key moments, the first being when Sonic & Shahra obtain the Water Blue Ring & Shahra cannot interact with the World Ring whereas Sonic can due to not originally being from the Arabian Nights[1], the second being that the World Rings still existed even after the Arabian Nights was completely destroyed by Alf Layla Wa-Layla with a few of them escaping from the eldritch monster, exposing themselves to the void unaffected before entering Sonic to transform him into Darkspine Sonic[2], showcasing that they are this independent from the reality the govern.
"shape all of reality within their area of influence and at whatever level that area exists in"
There are a number of statements/feats which showcase the World Rings shaping the World of the Arabian Nights. They are stated by Erazor Djinn to be the force which binds the pages of the Arabian Nights as well as make up the stories which exist within it[2]. The World Rings' authority over the Arabian Nights reality is so absolute that even their incomplete power as a result of Erazor Djinn failing to kill Sonic in order to obtain control can completely destroy the Arabian Nights[2], with Alf Layla Wa Layla intending to recreate the Arabian Nights in his own image[2]. Furthermore, Darkspine Sonic with only 3 of the World Rings was able to restore the Arabian Nights with a mere hand gesture[2], highlighting how the World Rings shape all of existence within the Arabian Nights & can even recreate it.
Summary[]
We can deduce that the World Rings are independent to the Arabian Nights to a degree that those who originate from cannot interact & can persist even after the reality which they govern, the Arabian Nights is destroyed as well as them being the force which binds & shapes reality, allowing users to reshape the world in their image & even destroy it.
With this, we can conclude that the World Rings & those who use their power are granted Conceptual Manipulation (Type 1).