Structure is the controller.

A periodic structure earns its name when where a thing sits tells you how it behaves. For state, the dimensions are the formalism it is held in, how it composes, how it advances, where its boundary is, what triggers a step, what the machine knows of itself, what each transition costs, what can be checked about it, and how long it lives.

Read across the coordinate and the system explains itself — what it can express, what it can verify, what survives a restart, what it pays per transition in joules. The same map covers a finite-state machine, a hierarchical statechart, an entity-component system, an actor supervision tree, a Petri net, a DEVS simulation, a behavior tree, an operating-system kernel, a TLA⁺ specification, and an agent orchestration graph.

The map is a way of seeing, not a verdict. It classifies what runs, makes the structure of the design space legible, and lets a system be reasoned about before it is built — the same move the sibling stacks make for computation, information, synthesis, and data.