On the algebraic structure of a perspectival system

Preliminary sketch of a research programme. Deductive consequences of a minimal set of rules imposed on a system containing an observer, within what I call the polarized spacelessness. No spacetime manifold, metric, quantum postulate, or symmetry group is assumed. The rules force an involution, and bilinearity of the evolution operator. The resulting algebraic structure has mixed signature. I work out some of its consequences, including particle statistics, dimensional constraints, and the form of the gravitational component. Several questions remain open.