Informational Topology in de Sitter Space: A Lemma and an Open Problem

We establish a rigorous lemma on the kernel of the BKM informational metric in even-dimensional de Sitter space: it is one-dimensional and generated by the Euler variation. This proves that topological degrees of freedom are informationally invisible to local geometric perturbations. We then formulate a precise conjecture connecting the Murray-von Neumann dimension of the modular kernel to the Euler characteristic of spacetime, and identify the obstacles to its proof. A possible connection to Connes' cyclic cohomology is indicated."