  We explore the operad of finite posets and its algebras. We use order
polytopes to investigate the combinatorial properties of zeta values. By
generalizing a family of zeta value identities, we demonstrate the
applicability of this approach. In addition, we offer new proofs of some of
Ramanujan's results on the properties of Eulerian numbers, interpreting his
work as dealing with series inheriting the algebraic structure of disjoint
unions of points. Finally, we establish a connection between our findings and
the linear independence of zeta values.
