While I can appreciate the sentiment regarding Abel and Galois, the impossibility of solving the general quintic by radicals has a strikingly different form. Its Galois group is not solvable, giving a precise obstruction to a solution by radicals. In your case, it seems less like an impossibility that two graphs could be the same and more like a claim that they are unlikely to be the same. Perhaps two path-dependent processes are unlikely to generate the same graph, but that is not the same as proving they cannot.
My own tendency is to think that a graph generated by material processes over a finite life may have only finitely many distinguishable configurations. That leaves open the possibility of collisions. The birthday problem or hash collisions seem like closer analogies to me. There also seems to be more work to do in showing why *consciousness* (whatever is meant by the word) should be modeled by an adjacency graph, and why a theorem about such graphs would resolve the hard problem.
.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. FRIAM Applied Complexity Group listserv Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
