Help, a term for distilled, common denominator, boiled down?

Help please! I'm looking for a term that I can use in a definition and description. I have a complex thing i'm describing and I've worked to remove all of the variables, the unrelated cultural connotations, the unimportant quirks, etc and I'm left with the raw essential. For example, let's say... show more Help please!
I'm looking for a term that I can use in a definition and description.

I have a complex thing i'm describing and I've worked to remove all of the variables, the unrelated cultural connotations, the unimportant quirks, etc and I'm left with the raw essential.

For example, let's say I'm trying to describe THE qualities of a dog. There are all kinds of dogs --some have are short, some are fat, some bark, some howl, some have three legs, some have long hair, etc..... but let's say I've narrowed it down to three qualities that make it a dog and only a dog and nothing else can share those three qualities, how might I describe this list of qualities?

I might say

1. Must be derived genetically from a wolf
2. Must be domesticated
3. Must love belly rubs

(yeah, I know my list above isn't accurate....it's an example of the material I'm working with).

I might use terms like
- The Platonic Dog
- The Quintessential dog
- The Typical Dog


None of these fit exactly. The word I need should demonstrate that I mean that my 3-part definition exactly and specifically describes the most boiled down, basic, and precise definition of a simple dog. Such dogs may have other qualities but those qualities are always in addition to this boiled down, basic form of dog.

Again, I'm not talking about dogs --- I'm just using dog as an example :)
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