Om written in Siddham is a single joined sign rather than three letters set side by side, and it is probably the most widely reproduced piece of the script anywhere. It is cut in stone, carved in wood, brushed on paper, printed on cloth, worked into metal and set at the head of texts, and it travels well outside the traditions that can read the rest of the syllabary. A great many people who have never seen another Siddham letter have seen this one.
The threefold analysis behind it is old and belongs to the Indian commentarial tradition rather than to the script. It takes the syllable to consist of a, u and m, and reads those three as a set that can be laid against other sets of three, a habit of the commentaries that later traditions extended in a great many directions. The script itself simply writes the syllable, as one sign; the analysis is about the sound.
Its reproduction raises a question this atlas keeps meeting. A sign lifted out of the tradition that uses it, printed on a product or worn as an ornament, is being read by almost nobody who could say what it is. The traditions that keep Siddham in use treat the syllable as belonging to a practice with conditions attached, and describing that is not the same as recommending it. What can be said plainly is what the sign is, where it comes from and what the tradition holds it to be, and that is what is recorded here.