The set of all possible transformations of all possible graphs, starting from all possible starting conditions, computed iteratively for all possible time
In order to establish a meaningful location in the ruliad, we need to impose an invariant for all observers in that perspective.
Please imagine this as perspectives embedded in perspectives, spaces within spaces.
Our imposed invariant is the number of incoming edges should equal the number of outgoing edges in these directed graphs. I call this "rank", and could use suggestions for a better term!
These are all Balanced Digraphs
The short version of what's going on here is I have cataloged all possible graphs ( n <= 6, k <= 6) by "rank" (k), meaning each row and each column have the same number of edges connected to it.
I have searched every possible matrix of each size and each rank above, and this is the full catalog of both morphologies and symmetries present in those structures
I have discovered 562 of these morphologies, representing 439,024 individual graphs of consistent rank, and determined the characteristic polynomial for all of those. This was via a full search of the entire space, and the charateristic polynomials were found via Laplace expansion.
I call two graphs the same morphology if their characteristic polynomials are the same.
This website currently exists for the purpose of passing this data along to the Wolfram Physics Project
This is an open source project and it can be found at https://github.com/dondrury/adjacency-matrix
This is a continuing work of love and passion that I believe will be of immense use to mankind. It has involved two years of work and many weeks of compute time.