PaxosLease in Relativistic Inertial Frames

Abstract

A lease grants one holder exclusive authority over a resource for a fixed term, and its safety property guarantees that at most one holder has the lease at any time. Under special relativity ``at any time'' has no frame-independent meaning for participants in relative motion. This note first restates the classical safety property with light cones, requiring a holder's expiry to lie in the causal past of any later acquisition by a different holder, an order every observer agrees about. Second, the paper modifies classical PaxosLease: the core change is that the containment and quarantine rules each gain a factor of $k = \sqrt{(1+β)/(1-β)}$, the relativistic Doppler factor, where $β$ is relative speed as a fraction of the speed of light.