OMG! Thank you for this generous rating! Speechless!

Made a video from the in-notebook animator for the two clock configuration with some light ticker:

https://youtu.be/Dvp_S66rCAc?si=VOgUMVNEOuFRoJju

The Ref [8] in the notebook innovated the Petri category and the proposed Petri Net evaluator is entirely Monoidal in nature!

I used that Monoidal structure to asynchronously sequence the String Rewriting Peal Axioms and actually perform additions and multiplications:

1. The Petri Net evaluator now being a monoid was easy to evaluate and tiny
2. I can easily add other monoids e.g. monoids generated by Simplex Monads
3. This new approach makes the Categories useful to program in Wolfram Mathematica as opposed to keep plotting arrows on top of each other. We now can learn from the Ref [8] paper how to implement Strict Monoidal categories in cooperation with the Petri category to enhance our understanding and breadth of de novo applications based upon Category theory. I shall bravely attempt to program Monads somehow into the 14.3 Mathematica and see if we could 5. make Mathematica interpret and evaluate subtle new algebraic systems not seen before! Also will code a rather forgotten paper by David Benson titled Category of Derivations , which examined the categoricity of the Rewriting Systems.
4. Finally, for super large Petri Nets, say thousands of Places and Transitions, the Monoidal version allows us to explore GPU applications in Wolfram Mathematica to deliver new classes of symbolic simulators at large scales.

Feel free to report bugs and mistakes in the theory, regards

Dara O Shayda Chief of Software Computational Classnotes Republic of Ireland