Busy Beaver–based bounds as physical laws of growth and convergence

Establish that, in our universe, directly measurable physical quantities obey the Busy Beaver–derived bounds on rates of change—specifically, that no such quantity can grow faster than Radó’s Busy Beaver function BB(n) or slower than its inverse BB^{-1}(n), and that no such quantity can converge to a finite value faster than 1/BB(n) or slower than 1/BB^{-1}(n)—thereby confirming these limits as genuine physical laws.

Background

The paper shows that assuming the physical Church–Turing thesis yields stringent asymptotic bounds on physically realizable growth and convergence, tied to the Busy Beaver function and its inverse and reciprocals. The author proposes elevating these derived bounds to the status of physical laws.

Validating this conjecture would link computability theory directly to empirical physics by asserting universal limits on growth and convergence across all directly measurable phenomena.