Hyperdimensional (HD) computing is a set of neurally inspired methods for computing on high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to effect a variety of information processing tasks. HD computing has recently garnered significant interest from the computer hardware community as an energy-efficient, low-latency, and noise-robust tool for solving learning problems. We present a novel mathematical framework that unifies analysis of HD computing architectures, and provides general, non-asymptotic, sufficient conditions under which HD information processing techniques will succeed.