The Physics Derivation Graph focuses on the following:

- Claim: a finite static directed graph exists which describes all of mathematical Physics.
- Claim: the graph representation is machine parsable
- Claim: validity of (some) derivation steps in the graph can be checked using a computer algebra system
- Claim: correctness of (some) derivation steps in the graph can be proven formally

As of May 2024 claims 1, 2, and 3 are demonsrated; work on 4 is planned.

Caveats:

- I’m not aware of currently available computer algebra systems are capable of validating all of mathematical Physics.
- The graph relies on manually checking the equivalence of expressions represented using Latex, Sympy, and Lean.

A novel result of this work has been the enumeration of inference rules used in mathematical Physics.

- Create a framework capable of describing all mathematics needed for physics derivations. PDG uses Latex as the syntax in the framework because Latex is how I think of equations. However, Latex is insufficient for processing by computer algebra systems. Status: proof of concept exists
- Create machine-readable databases which use the above framework to capture the mathematical derivations in physics. To hold the content of the databases I’m using custom XML. Status: proof of concept exists
- Create graphical representation of relations content in the databases. PDF uses d3js (previously GraphViz) to render the visualization. Status: proof of concept works
- Use a computer algebra system to verify the relations in the databases. PDG uses SymPy as the CAS. Status: proof-of-concept completed in 2020
- Create a web browser-based viewing of the generated graph. HTML5 seems capable. Status: proof-of-concept completed in 2020
- Create a web browser-based graph input tool. Status: proof-of-concept completed in 2020

The proof-of-concept for all the initial objectives were completed during the Covid-19 lockdown (summer of 2020).

- Use a property graph (e.g., Neo4j) and enable users to query the graph. Status: underway as of May 2024. See <
- Adapt visualizations to the new property graph database
- Adding content manually is burdensome. Find automations
- Eliminate website errors
- Enact testing of the backend software and the web UI.

Creative Commons Attribution 4.0 International License

http://www.apcjones.com/arrows/ and https://arrows.app/

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