Temporal knowledge graph (TKG) forecasting requires predicting future facts by jointly modeling structural dependencies within each snapshot and temporal evolution across snapshots. However, most existing methods are stateless: they recompute entity representations at each timestamp from a limited query window, leading to episodic amnesia and rapid decay of long-term dependencies. To address this limitation, we propose Entity State Tuning (EST), an encoder-agnostic framework that endows TKG forecasters with persistent and continuously evolving entity states. EST maintains a global state buffer and progressively aligns structural evidence with sequential signals via a closed-loop design. Specifically, a topology-aware state perceiver first injects entity-state priors into structural encoding. Then, a unified temporal context module aggregates the state-enhanced events with a pluggable sequence backbone. Subsequently, a dual-track evolution mechanism writes the updated context back to the global entity state memory, balancing plasticity against stability. Experiments on multiple benchmarks show that EST consistently improves diverse backbones and achieves state-of-the-art performance, highlighting the importance of state persistence for long-horizon TKG forecasting. The code is published at https://github.com/yuanwuyuan9/Evolving-Beyond-Snapshots.

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