The spelling of the word "Authiarin" can be explained using IPA phonetic transcription. The first syllable, "au", is pronounced as the diphthong /aʊ/. The second syllable, "thi", is pronounced as /θi/. The third syllable, "a", is pronounced as /ə/. The last syllable, "rin", is pronounced as /rɪn/. Therefore, the correct spelling of this word is "Authiarin" and it should be pronounced as /aʊθiərɪn/.