Where does “pith” come from?

I appreciate the challenge, but I need to flag a critical issue with this chain: it doesn't coherently support the word "pith." The chain shows: - English pi - Ancient Greek πεῖ (pei) - Proto-Germanic -iþō - Proto-Indo-European -ti/-tós This appears to be a suffix chain (note the hyphens in Proto-Germanic and PIE), not a word etymology. "Pith" as a noun (meaning the soft tissue in plant stems, or figuratively, the essential part) has a completely different origin—it comes from Old English piþa/pyþa, from Proto-Germanic *piþōn, not from a Greek suffix. **I cannot write an accurate one-sentence summary from this chain because the chain itself doesn't support the headword "pith."** Could you verify: 1. Is this the correct

pith (English): The soft, spongy substance in the center of the...

Definitions

  1. The soft, spongy substance in the center of the...

Ancestry of “pith”, step by step

pith traces back through 3 separate lines of ancestry.

via English helmet

StepLanguageWordMeaning
1EnglishhelmetA protective head covering, usually part of...
2Middle EnglishhelmetA helmet; an armoured piece of headgear
3Old Frenchhelmet
4Old Frenchhelmehelmet
5Medieval Latinhelmushelmet
6Frankishhelmhelmet
7Proto-Germanichelmazhelmet
8Proto-Germanichalmazhalm; stem; stalk; straw; hay
9Proto-Indo-Europeanḱolh₂mosstalk
10Proto-Indo-Europeanḱelh₂-to pierce, strike; to stick; prick; stab

via English Pi

StepLanguageWordMeaning
1EnglishPiThe sixteenth letter of the Classical and Modern Greek alphabets and the seventeenth in Old Greek
2Ancient GreekπῖAlternative form of πεῖ
3Ancient Greekπεῖpi, the name for the sixteenth letter Π, π of the...
4Proto-Semiticpay-the mouth

via Middle English pith

StepLanguageWordMeaning
1Middle EnglishpithThe soft interior portion of something,...
2Old Englishpiþapith
3Proto-Germanicpiþô
4Proto-Germanicpiþō

Words derived from “pith

Every word from Proto-Indo-European ḱelh₂-