In 1990, working with his wife Lloydine Arguelles, he devised the Dreamspell calendar, a perpetual thirteen month, twenty eight day system he presented as a synchronization tool distinct from, and in his account more universally applicable than, the historical Maya calendars it drew loosely on. The calendar assigns each day a named and numbered position, the material the atlas catalogues as the Dreamspell kin; the specific artwork associated with each position is gated to the Arguelleses and to the Foundation for the Law of Time as its publisher.
Arguelles founded the Planet Art Network and the Foundation for the Law of Time to promote Dreamspell and the broader calendar reform project he called the Law of Time. He remained active in that project for the rest of his life and died on 23 March 2011, at seventy two. Mainstream Mayanist scholarship does not treat Dreamspell as a continuation of the historical Maya calendar systems, regarding it instead as a modern invention loosely inspired by them. After his death in 2011 his widow Lloydine and their successor organizations continued to promote Dreamspell and the wider Law of Time project, maintaining an active practitioner community that still marks 26 July each year, the Dreamspell new year, as its central annual observance.