It’s theoretically impossible to create a system to remember every human that doesn’t rely on external storage.

I’ll explain: let’s say that for every human that dies, they will be remembered and live on in the heart of another, living human. Each living human can remember n dead humans.

we can set up an equation

pn >= r

where p is the current population of live humans, r is the amount of dead humans that must be remembered.

We can express the rate of deaths as a proportion of the current living population:

d/dt[r] = pb

Where t is time and b is the instantaneous death rate per captia with respect to time (generally a constant).

Combined with the previous, we get the separable differential equation:

d/dt[r] = pb >= (r/n)b

dr/dt >= rb/n

[1/r] rt >= [b/n] dt

Integrated:

ln|r| >= tb/n+C

r >= e^(tb/n+C)

pn >= r >= e^(tb/n+C)

p >= e^(tb/n+C)/n

So in order for this system to work, the living population must always be growing exponentially, which is not feasible for modern humanity.