Where does “hone” come from?

I appreciate the detailed instructions, but I need to flag an issue with this chain: the intermediate steps don't form a coherent etymological path from the headwords to the final PIE roots. The chain shows multiple unrelated PIE roots (ḱeh₃i-, ḱm̥tóm, ḱwn̥tós, ḱwṓ) without clear connections explaining how "hone" derives from any of them, and the Middle English and Old English forms listed (oon, ān) don't obviously relate to "hone." Before I write the summary sentence, could you clarify: - Is this chain complete and accurate as intended? - Should "hone" trace through one specific PIE root rather than multiple? - Are the Old English and Middle English forms correct? A well-formed etymology summary requires a genuine etymological chain, which this doesn't appear

hone (English): A sharpening stone composed of extra-fine grit...

Definitions

  1. A sharpening stone composed of extra-fine grit...

Ancestry of “hone”, step by step

hone traces back through 3 separate lines of ancestry.

via English wort

StepLanguageWordMeaning
1EnglishwortA plant; herb; vegetable; Any of various plants...
2Middle EnglishwortA plant; Wort or an analogous mixture
3Old Englishwyrtplant; herb; wort
4Old Englishbisċopbishop
5Latinepiscopusan overseer, supervisor, bishop in a Christian...
6Ancient Greekἐπίσκοποςwatcher, guardian; scout, watch; overseer,...
7Ancient GreekἐπισκοπέωI watch over
8Ancient Greekἐπι-on, upon, on top of, all over, covering; on,...
9Ancient Greekἐπίas well, besides; For usage in composition, see...
10Ancient GreekἩμέρα
11Ancient Greekἦμαρday; by day; midday
12Proto-Hellenicā́mərday
13Proto-Indo-Europeanh₂eh₃mr̥heat
14Proto-Indo-Europeanh₂eh₃-to be hot; to burn

via Middle English hon

StepLanguageWordMeaning
1Middle EnglishhonAlternative form of honen; Alternative form of...
2Old IrishúainAlternative spelling of úainn; time, leisure
3Old Irishúanlamb; foam; froth
4Proto-Celticognoslamb
5Proto-Indo-Europeanh₂egʷnóslamb
6Proto-Indo-European-nósCreates verbal adjectives from roots

via French hogner

StepLanguageWordMeaning
1Frenchhognerto grumble

Words derived from “hone

Every word from Proto-Indo-European h₂eh₃-