Joseph Natal

activity

20242026

collaborators

4 papers

math.CO2026

A Spanning Subgraph of Conway's 99-graph

Joseph Natal, Oleksiy Al-saadi

We show that in any hypothetical $G$ = srg(99,14,1,2) a spanning subgraph with $189$ edges is forced. Moreover, the graph formed out of the remaining edges has the spectrum $(12^1,…

math.CO2025

Diameter Constraints in 2-distance Graphs

Oleksiy Al-saadi, Joseph Natal

For any finite, simple graph $G = (V, E)$ , its $2$ -distance graph $G_{2}$ is a graph having the same vertex set $V$ where two vertices are adjacent if and only if their distance is $2…

physics.hist-ph2024

Refuting the Metaphysics of Wolfram and Tegmark

Joseph Natal

Wolfram's hypergraph dynamics should replace outmoded models in physics. This should even more so be the case if experimental evidence for the theory is found (which I believe is p…

cs.CC2024

Fast Simulation of Cellular Automata by Self-Composition

Joseph Natal, Oleksiy Al-saadi

Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional t…