Timelets on causal sets

TL;DR

This paper introduces and analyzes timelets, dual structures on causal sets that serve as discrete global time coordinates, exploring their algebraic, geometric, and combinatorial properties.

Contribution

It presents the concept of timelets on causal sets, characterizes them via incidence matrices, and links them to preclusive coevents, revealing their decomposition and simplicial complex structure.

Findings

Timelets are characterized by incidence matrices.

Each timelet uniquely decomposes over preclusive coevents.

Equivalence classes of timelets form a simplicial complex.

Abstract

Dual structures on causal sets called timelets are introduced, being discrete analogs of global time coordinates. Algebraic and geometrical features of the set of timelets on a causal set are studied. A characterization of timelets in terms of incidence matrix of causal set is given. The connection between timelets and preclusive coevents is established, it is shown that any timelet has a unique decomposition over preclusive coevents. The equivalence classes of timelets with respect to reascaling are shown to form a simplicial complex.