True, but I don't think it would stay a gas giant all that long, the CO2 would solidify once it got cold enough as would the neon.

That would presumably leave a huge lump of dry ice / neon ice with a dirty great big rocky core.

What the heck would that be classified as?

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God: I refuse to prove that I exist. For proof denies faith and without faith I am nothing.
Man: But the Babel Fish is a dead giveaway isn't it? It proves you exist and so therefore you don't. Q.E.D.