Lev,
Ever since being introduced to your work, I have wondered if I could be persuaded that a more fundamental structure than the integers underlies the idea of order. I was taken by your coinage, "struct", and its description, almost immediately. Structs seem to fit naturally with the kind of "black box" relation that characterizes a system of components evolving at different rates (like the Ashby/Bar-Yam multiscale variety)*; the internal evolution of the black box is unavailable, but the time dependency of the network forces a visible relation among hubs of coordinated activity**, such that even though the system state shows little change in the aggregate of elapsed time, at any two particular adjacent time measures, the locations of central hub activity may differ radically. (Cf. Gould-Eldredge punctuated equilibria^ for a connection to evolutionary biology, and self-organized criticality^^ in the extended model of evolution.)
If black boxes are structs and structs are nodes, network vertices are time paths, which leads to the important conclusion that you and I share: time is identical to information. In such a network, information is physical (quantum information)accounting for dynamic activity. In other words, the time we measure is independent of the internal "black box" time; the struct is self contained and independent of the network and only enters via a time-dependent relation of measured quantum information.
I understand the lack of evolutionary potential in your "non-structural point." However, what always hangs me up when I engage with your work, is that points of the complex plane are not "non-structural." Points are analyzed as lines in complex analysis, and the complex plane compactified with one point at infinity (Riemann sphere) _does_ give us space and content; i.e., the algebra is closed and the space has dimension 2. From the chaotic field of non-ordered complex numbers, we do get ordered relations in real time and space, from analysis on the Hilbert space. I still don't grasp what in your concept would obviate such a mathematical approach.
Tom
*Bar-Yam, Y. [2003] "Multiscale Variety in Complex Systems," NECSI Technical Report 2003-11-01 (Nov.)
**Braha, D. & Bar-Yam, Y.[2006]. "From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks." Complexity vol 12, no 2, pp 59-63
^Eldredge, N., & Gould, S. J. [1972]. "Punctuated equilibria: an alternative to phyletic gradualism." In: Models In Paleobiology (Ed. by T. J. M. Schopf). Freeman, Cooper and Co.
^^Bak, P. [1996]. How Nature Works: The Science of Self-Organized Criticality. Copernicus.