Dependence of Viterbo spectral diameter boundedness on coefficient rings

Determine whether there exists a closed manifold for which boundedness of the Viterbo spectral diameter depends on the choice of coefficient ring.

Background

The paper studies the boundedness of the Lagrangian spectral diameter in the space of exact Lagrangians Hamiltonian isotopic to the zero section of a disc cotangent bundle. Its main theorem proves unboundedness under topological and geometric hypotheses involving nontrivial first cohomology, nonvanishing Euler characteristic, and the existence of a metric without conjugate points.

The authors emphasize that the coefficient ring plays a significant role in the argument and compare this phenomenon with coefficient-dependent behavior already known for Hamiltonian spectral norms. They ask whether boundedness itself can vary with the coefficient ring for a single manifold; the paper does not provide such an example or resolve the question.