How and in what manner is an object defined as "existing"? What principles are followed to deem some object as tangible or real, and not imaginative? Please answer.
Technically speaking, all objects are imaginative, because our mind constructs objects from a complex reality in order to aid cognition.
Think about a fist. Is it an object? Many people would say so, because it can punch and break things. But what happens to a fist when you open it? The object you thought was so real suddenly isn’t there - it morphed into something else.
This is the nature of all reality - everything is in constant flux, and things we perceive as physical objects are temporary arrangements of matter, arbitrarily named and categorized by our mind so we don’t get lost in complexity.
So to answer your question - all objects are indeed imaginative and as long as you can think of them, they exist. Whether they also exist on the physical observable reality is a question of scientific measurements of weight, volume, mass and / or other properties, but we’re entering the realm of physics here.