Where does “egocentric” come from?

I need to identify what went wrong with this chain before writing the sentence. The chain shows: - English ego → Ancient Greek κεντρικός (kentrikós, "central") → Proto-Indo-European éǵh₂ → Proto-Indo-European éǵh₂ (repeated) This chain is problematic. Ancient Greek κεντρικός doesn't etymologically connect to ego. The Greek word comes from κέντρον (kentron, "center/point"), not from a form meaning "I/self." Also, the chain ends with the same PIE root listed twice, which suggests incomplete or corrupted data. Given the rules state "State only what the chain supports. Do not invent dates, cognates, or intermediate steps," I cannot write an accurate sentence because the chain itself appears corrupted or incorrect. However, if I must work with what's given literally

egocentric (English): selfish, self-centered; Egotistical; Relating to...