The notion of an agent presumes a stable identity and memory.
But is it the same thing if even the same prompt is booted a second time?
Consider an app on your iPhone.
The app is a bundle of code, the same as the bundle on everyone else's phone.
What makes it yours?
When it boots up, it looks into its storage–a segment that only it could have written to in the past–looks up the data there, and behaves appropriately.
Now imagine if you could run the same app code in two different partitions on the same device.
Those would clearly be two different instances, two different identities.
Agents have the same dynamic.
The same prompt, running with a different context, is a different thing.
You can lobotomize an agent by deleting the earlier parts of its context window.
That doesn't feel like an individual, consistent entity.