Is the ARC Bound like the speed of light for AI scaling?

The analogy is tempting, and it fails in the way that matters most. The speed of light is an established, measured constant that nothing is observed to cross. The ARC Bound is a proposed stable limit, alpha no greater than 2, on a different kind of quantity: the scaling exponent of a self-improving system's capability under the condition that its internally generated correction keeps pace. It is a scaling limit, not a speed limit. It bounds how much growth self-correction can carry, not how fast anything moves or happens.

The second difference is what crossing means. Nothing crosses the speed of light; that is the point of it. Systems can cross the ARC Bound. The framework's claim is that a system whose correction is generated internally cannot remain stably self-correcting beyond it: crossing is supercritical, and the predicted consequence is correction lag, accumulating deviation and drift, not an instant wall. That is why the recorded refutation condition is strict in exactly the opposite direction to a physical constant: an exponent above 2 sustained without loss of stability would refute the ARC Bound.

Where the analogy points correctly is at the shape of the claim, not its status. Like a physical limit, the number two is derived rather than fitted: if internally accumulated correction strengthens at most like the square root of what it has accumulated, and stability requires correction to keep pace with capability, the fastest correctable growth is the reciprocal of one half. But the speed of light has survived a century of measurement, and the ARC Bound has not yet been measured at all: it is proposed, the one working assumption is stated, and the deciding measurements are written, dated and prepared as draft registrations awaiting human submission.