Current LLM-based agents demonstrate strong performance in episodic task execution but remain constrained by static toolsets and episodic amnesia, failing to accumulate experience across task boundaries. This paper formalizes the Self-Evolving Agent (SEA) from the perspective of digital embodiment and continuous cross-task evolution, introduces the Evolutionary Flywheel as its minimal sufficient architecture, and presents SEA-Eval -- the first benchmark designed specifically for evaluating SEAs. Grounded in Flywheel theory, SEA-Eval establishes SR and T as primary metrics and, through sequential task stream design, is designed to quantify evolutionary gain, evolutionary stability, and implicit alignment convergence. Empirical evaluation reveals that, under comparable success rates, token consumption differs by up to 31.2 times between frameworks on individual tasks, with divergent evolutionary trajectories emerging under sequential analysis -- demonstrating that success rate alone creates a capability illusion and that the sequential convergence of $T$ is the key criterion for distinguishing genuine evolution from pseudo-evolution.