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You parent-child relationship seems backwards from most/all GTD implementations I've seen. An action (or the project itself) that is dependent of one or more other actions is usually listed above the other actions.

Your theory implies each action is only dependent on one immediate (previous) action. If you have to perform A, B, and C (in any order) before Z, can you explain how your tree structure would be defined?

Also, I'm not sure I follow your "only parallel projects" idea. If I have to do A, then B, then C, your tree would look like:

A
>B
>>C

This is a sequential project that is defined by the tree organization. Then a parallel project (where B or C can be done in any order, before A) would look like:

A
>B
>C

But the problem (as I mentioned above) is what if A or B can be done in any order and C done last. By your definition, A and B would be at the same level. Where do you put C?