The Object Lifetime Tree

• Attempting the First Process

See i for figure of a simple representation of an object transformation through 5 processes.

Embedded in ${\phi }_0^4$ are $P_0\dots P_4$. I trail off here with a weak attempt to show the functional path from the ultimate output leading back to the initial creative process, $P_0$

You can see that the complete state of ${\phi }_o^4$ is dependent wholly on the flow of objects through the processes $P_0\dots P_4$. This is important, assuming a compete model, i.e. ${\Phi }^{\prime }=\varnothing$, then any intermediate object ${\omega }_k$ can be entirely described as a function of processes.

see ii for a figure of the Object Lifetime Tree for ${\phi }_0^4$.

Embedded into the very structure of ${\phi }_o^4$ are the processes it underwent to reach its present state.

But of course process 0 is not itself static and the nature of its products can change.

The framework grows, but the historical state must not be invalidated as a result. The complete process history must be representable. There is also a Process Lifetime Tree.

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Is it in the encoding of ${\phi }_o$ that enables us to discover its lifetime?

I think the key is in that we are looking at the object always in context of some known local history. So we can query from output to input. How do we then acquire the context of the previous process in the tree?

I think it must be necessary that the process in question leaves an indelible mark upon the object. We are asking for some objective state for how we go from input state to output state. The only answer I have is that processes overlap. That the Output State is bound up with the Input State .

Somehow ${\phi }_i^x$ is bound to ${\phi }_o^y$.