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| Awesome work! Very much looking forward to being able to extract discrete higher homotopy groups for graphs based on more general tessellations... |
| An interesting and subtle question! Of course, our model is only deterministic up to measurement. As detailed in my quantum mechanics paper (https://www.wolframphysics.org/technical-documents/) different choices of quantum observation frame,... |
| Is this thread a duplicate of https://community.wolfram.com/groups/-/m/t/1950038 ? Anyway, as I explained in your other thread regarding this topic, layered digraph embedding for acyclic graphs is a well-defined optimization problem, and hence the... |
| Neat idea, but I'm not sure that I like the concept of having hypergraphs with such large edge density! (not least because it leads to an unbounded Hausdorff dimension for space...) See my comment on this related post... |
| Energy conservation (which, as mentioned above, is violated cosmologically) only places constraints upon the flux of causal edges associated with updating events which maintain baryonic matter in the hypergraph, which in turn only places constraints... |
| In the relativity paper, I say "If one now considers performing a layered graph embedding of a causal graph..." Layered digraph embedding (at least for acyclic digraphs) is a well-defined optimization problem, in which all edges are given by... |
| Cool post, but I think that there may be some misunderstanding behind what you've written here. The metric induced on our hypergraphs is _not_ the combinatorial metric (since clearly, as you say, this does not satisfy even the basic axioms of a... |
| We are working on introducing a regular progress bulletin, that you will be able to subscribe to, within the next week or so! Also, I'm intending to start posting the results of our various working sessions onto community very soon, so that you guys... |
| Cool idea! Effectively you're defining a generalization of the notion of a critical pair or branch pair to a "critical tuple" or "branch tuple". Of course, as I outline in my papers (https://www.wolframphysics.org/technical-documents/), there is... |
| [The Wolfram Summer School Fundamental Physics Track][1] Are you an advanced research-oriented student in mathematics, theoretical physics or theoretical computer science, who wants to make potentially cutting-edge contributions to our... |