A computation is mortal if halting it dissolves the boundary that individuates it, over some finite time horizon. Every clause in that sentence is doing work, and the horizon clause is doing the most.
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The previous page took away an easy distinction. We cannot say biological minds are self-contained while artificial ones are hosted, because nothing is self-contained. Every finite thing is held in conditions it did not make.
That leaves a sharper question.
If everything is hosted, what makes a living computation different from an ordinary calculation running inside a host?
The answer cannot be that the living system has a body, because bodies are not the point. It cannot be that the system depends on the outside, because everything does. It cannot be that the system is fragile, because many fragile things are not alive. A soap bubble is fragile. A vase is fragile. A snowflake is fragile. None of them owns a loss function.
The difference is not fragility. It is participation.
A living system participates in maintaining the boundary that makes it a system. It is not merely located inside a boundary. It helps keep that boundary going. Its sensing, acting, repairing, eating, moving, attending, avoiding, seeking, and regulating are all part of the process by which it remains itself.
That is the sense in which a computation can be mortal.
Here is the definition this arc needs:
A computation is mortal if halting it dissolves the boundary that individuates it, over some finite time horizon.
Equivalently: the system's boundary is an output of its own inference.
This definition is deliberately narrow. It is not a definition of consciousness. It is not a definition of intelligence. It is not a definition of value. It says only when a computation is part of the maintenance of the system that the computation individuates.
A spreadsheet can stop calculating and still be the same spreadsheet file tomorrow. A paused video game can sit on a disk. A saved model can wait in storage. Nothing about the file's boundary depends on the file actively predicting, regulating, or repairing itself. The computation can halt without the system dissolving, because the system was never maintaining itself by computing.
A cell is different. Stop the right processes long enough and the cell does not merely pause. Its gradients collapse. Its membrane stops doing the work that made inside and outside distinct. Chemistry that was organized becomes chemistry that is just happening. The boundary that made the cell a cell dissolves.
A body is different in the same way. Stop metabolism, circulation, respiration, repair, immune regulation, temperature control, and neural coordination long enough, and the body does not remain a sleeping person. It becomes a corpse. The outline may stay for a while. The boundary, in the relevant sense, has failed.
The computation was not sitting inside the system like a passenger. The computation was one of the things making the system be there.