Cyaegha
Please understand that I'm not trying to be mean here. You mention you've been applying for grants to work on this, but if you don't explain the mathematics adequately or demonstrate how it differs from existing formalisms then I imagine people are just going to reject you instantly. I would suggest seriously trying to formalise some of this stuff in a proof assistant like Coq. That'll quickly tell you if your theory works or not.
Yes obviously, but nowhere is it clear that you actually have a lattice of any kind. Specifically, I see no reason why pruning DAGs of unused computations would yield a lattice, and this is a result you seem to rely on. Program lattice does indeed sound nicer than program bounded poset, but I would be more wary about misusing terminology than having a nice name! :)
A lattice is a partial ordering with a single unique "top element" (least upper bound) and a single unique "bottom element" (greatest lower bound). Every node in the lattice is reachable by following some directed path from the single least upper bound, and there is a directed path from every node in the lattice to the single least lower bound.
A lattice is a poset where binary joins and meets exist. You define a bounded poset not a lattice. In general a lattice need not have either a top element or a bottom element, although all finite lattices are complete and thus do have top and bottom elements. The second sentence is also redundant, because for any element x of a lattice x ≤ ⊤, so why talk about paths?
Consider the argument for his proposed language being Turing complete on the flow manifesto page. He claims that this follows from the Böhm-Jacopini theorem. However the Böhm-Jacopini theorem requires variable assignment is allowed in the subprograms (which does not appear to be the case in flow), and without this the theorem does not hold, as this paper by Kozen demonstrates: www.cs.cornell.edu/~kozen/papers/bohmjacopini.pdf. Then he goes on to argue that order duality implies the existence of a selection operator in flow, which doesn't seem to make any sense.
I think it's telling that he has been working on this since 2010, yet has no decent proofs of his claims, nor any working implementation.