The spelling of the word "archphilosopher" is not commonly encountered and may be subject to a range of transcriptions. However, one possible representation is /ˌɑrk.fɪˈlɑs.ə.fər/. This is because the prefix "arch-" is often pronounced with the "k" sound, and the word "philosopher" is typically broken down into syllables as "phi-los-o-pher," with the emphasis on the second syllable. Overall, this complex term requires careful attention to its constituent parts to be accurately spelled and pronounced.