Where does “hardwood” come from?

I need to carefully work through this chain, but I notice there's a problem: the chain provided doesn't make coherent sense for the word "hardwood." The chain shows: - English hard | Middle English wood | Old English wudu | Proto-Indo-European weh₂t- | Proto-Indo-European kert- | Proto-Indo-European kert- | Proto-Indo-European weydʰ- This appears to conflate two separate etymologies (one for "hard" and one for "wood"), with "wood" traced through Old English wudu. However, the PIE roots listed don't clearly correspond to either "hard" or "wood" in standard etymological sources. Additionally, I'm told the known meaning is "(unknown)," which makes it impossible to weave in "the oldest one to explain the sense development" as instructed. **I cannot write an accurate one-sentence

hardwood (English): The wood from any dicotyledonous tree, without...