Boolean Algebra Is All That Is Required: An Infinitely Extensible Multiplexer Fabric as a Unified Model of Computation

Build a computational substrate from only wires, constants, and 2:1 multiplexers, then allow feedback and replication. Digital computation is routinely explained through many formalisms (machines, grammars, lambda terms), while hardware practice already runs on a simpler invariant: a clocked next-state function over bits. A single omission keeps the public model fractured: sequential switching networks—and the fact that reconfiguration is itself a Boolean, clocked process. This paper defines an explicit model in which (i) every primitive is Boolean (multiplexers, wires, constants), (ii) time is only state-to-state transition over registers realizable by those same primitives, (iii) “programming” is the installation of constraints into configuration registers, and (iv) unbounded memory is obtained by unbounded tiling (including physical self-assembly as one admissible growth mechanism). Under these assumptions the model is equivalent in power to standard universal models while remaining a single, uniform Boolean transition system.