Concept
Digital root
Add a number’s digits until one digit is left: 5432 becomes 14 becomes 5. The result is the remainder on division by 9. It is the central tool of Philomath.
Illustration made for this site. Not a photograph of the claim.
The operation is real arithmetic and has uses in checksums. Grant and Ghannam use it to sort numbers into three families, [1, 4, 7], [2, 5, 8], and [3, 6, 9], and then pair those families with forces, particles, and musical notes. Every multiple of 9 reduces to 9, which is why so many traditional time numbers, 25,920, 432,000, 86,400, land there: all are built from 60s and 360s, which are multiples of 9. The pattern is a property of base-60 bookkeeping before it is a property of the cosmos.