Where does “icebox” come from?

I need to carefully analyze this etymology chain, but I notice there's a problem: the chain provided doesn't actually trace "icebox" - it appears to trace "box" and contains some circular or confused elements (Latin buxus appearing after Ancient Greek, Proto-Indo-European h₁ésmi not matching the pattern, etc.). However, following the instruction to "state only what the chain supports" and not invent, I cannot write an accurate one-sentence etymology for "icebox" based on this chain, as the chain doesn't clearly support the full word. If I'm meant to work with what's given despite the issues, the most honest approach is: Icebox derives from English box, though the provided chain's etymology is unclear and contains inconsistencies that prevent a reliable summary. But this violates the format rules. Could you verify the etymology chain? A proper chain for "icebox" should show: English

icebox (English): A box or compartment containing ice; A...