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Were it to be confirmed, would "Planet 9" actually be classified as a Dwarf Planet?

It's estimated to have 10 times the mass of earth, putting it up in the Uranus and Neptune range: https://en.wikipedia.org/wiki/Planet_Nine#Size_and_compositi... .

Size isn't sufficient though. It also needs to have cleared its orbit.

It's orbit is thought to range between 200 and 700 AU, which is well outside the Kuiper belt at 30-50 AU and well inside the Oort cloud at 2,000-200,000 AU. So barring the discovery of more stuff in that area it seems to qualify.

Would that explain why there's a gap between the outside of the Kuiper Belt and the inside of the Oort Cloud?

That would be well beyond my knowledge or ability to say.

It certainly seems plausible, it may even explain the existence of the Kuiper belt, being held in the balance between Neptune and this planet much like the inner belt is by Mars and Jupiter.

Probably a planet. The distinction between planet and dwarf planet turns on whether the body has demonstrated gravitational dominance. Planet Nine's existence (if it indeed exists) was inferred from alignments of other bodies' orbits, which makes for a very, very strong case that it's a planet and not a dwarf planet.

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