Where does “paddy” come from?

I need to carefully analyze this chain, as something appears problematic. The chain shows "paddy" deriving from Latin "patres conscripti" (enrolled fathers), which then goes back to Latin "pater" (father) and Proto-Indo-European roots. However, this contradicts the earlier steps showing Proto-Malayic "padi" (rice field) and Proto-Malayo-Polynesian "pajay." These are actually two different etymological paths that cannot both be correct for the same word. The chain as presented is contradictory - it shows paddy coming from both Malayic languages AND from Latin simultaneously. Given the known meaning of English "paddy" (rice field), and that Proto-Malayic "padi" means rice, the Austronesian branch is the authentic etymology. The Latin branch appears to be an error in the chain provided. However, following your instruction to "state

paddy (English): Rough or unhusked rice, either before it is...