LifeSage: Existence-aware temporal graphs with multi-interval Lifespans

Classical temporal graph models represent dynamics by allowing edges to appear and disappear over time while implicitly assuming that the underlying vertex set remains fixed. This assumption conflates fundamentally different phenomena, namely behavioral inactivity and structural non-existence of entities, and may lead to inaccurate representations in systems where vertices temporarily or permanently disappear and later reappear.
In this work, we introduce LifeSage, an existence-aware temporal graph framework in which vertex existence is treated as a time-dependent quantity. Each vertex is associated with a multi-interval lifespan, enabling explicit modeling of intermittent, cyclic, and irreversible presence patterns. Temporal snapshots are interpreted as projections onto the set of existentially valid vertices, leading to masked adjacency representations in which non-existing entities are structurally excluded rather than treated as inactive.
We further distinguish between continuous flows, which require simultaneous existence of both endpoints, and discrete (transit) flows, which may persist independently of endpoint existence. This distinction allows temporal snapshots to violate the classical incidence condition and motivates an existence-aware masking perspective. We also discuss snapshot equivalence, event times, and representative generator snapshots arising from structural transitions in the graph. Finally, we outline how the proposed framework may support existence-aware temporal representations and learning settings on dynamic systems with evolving entity sets.