A Neighborhood of Infinity: Self-referential logic via self-referential circuits

An exploration of the formal similarity between delay-latch electronic circuits and provability logic (GL). The author shows that a specific delay component satisfies the same algebraic properties as the box operator in GL, including the fixed point property and an analogue of L\"{o}b's theorem. This isomorphism means that theorems of letterless GL correspond exactly to circuits that output an all-1s bitstream. Applications include reasoning about self-terminating programs and robot strategies in the iterated prisoner's dilemma. A companion open-source library in GitHub implements the syntactic approach using tableau methods and Craig interpolation.