Johann Weyer's Pseudomonarchia Daemonum (1577) catalogues sixty-nine demons. The Ars Goetia, compiled into the Lesser Key of Solomon a century later, lists seventy-two, minus Pruflas, plus four, reaching the sacred number of the Shem HaMephorash's seventy-two-letter name of God. The ranks mirror feudal hierarchy exactly, and most demons offer instruction: astronomy, geometry, rhetoric, medicine, the liberal arts of hell. Mathers and Crowley published the standard edition in 1904; Joseph Peterson produced the critical edition.
The grimoire story as practitioners lived it: Solomon commanded these spirits with a brass vessel and a ring, and the Goetia is his personnel file. To know a demon's name, seal, and rank was to hold its contract. Renaissance magi copied seals the way lawyers copy precedents.
The occult-revival reading: the seals function like glyphs of an addressing system, each one a signature that routes intent to a specific intelligence. In chaos-magick terms, the hierarchy is not hell's court but the mind's own departments, externalized so they can be negotiated with. The demon of astronomy teaches astronomy because you assigned it the job.
Weyer's 1577 catalogue lists sixty-nine demons. The Goetia lists seventy-two. The number was reverse-engineered to be sacred. If the arithmetic is admitted to be rigged, what else in the catalogue is?