Diamond Bracket Forms and How to Count to Two

This paper recasts George Spencer-Brown's laws of form as a bracket algebra, and add two new forms denoting paradox values. It states three axioms of these diamond bracket forms, and points towards a proof of completeness of those axioms. It also proves that the resulting diamond logic is fully self-referential; any self-referential system of diamond bracket forms has at least one solution. This paper then investigates the modulator circuits of George Spencer-Brown and Louis Kauffman; by applying diffraction, an operation unique to diamond logic, it proves that both circuits are circular rotors; they count to two by pushing paradox values around a loop.