Why Does Nature Count? The Eigenspectrum of Integers

What are integers, where do they come from, and why does nature count in them across all scales? This paper, 6th in a series, concludes with an answer: They are the eigenspectrum of a closure operator—the discrete set of values a winding process must take when return to identity is required. Integers are not primitive objects that mathematics simply assumes and physics borrows. Across 23 orders of magnitude, the integers arise from the same mechanism: a closed 1-form on a domain with a topological obstruction, whose periods are integer by Stokes' theorem. The integers are not counted. They are forced. The primes emerge as the irreducible modes. In this light, the Riemann zeta function is not a curiosity of analytic number theory but the partition function over topologically primitive closure modes.