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.

Goals / Objectives

Initial Objectives

[x] 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
[x] 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
[x] Create graphical representation of relations content in the databases. PDF uses d3js (previously GraphViz) to render the visualization. Status: proof of concept works
[x] 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
[x] Create a web browser-based viewing of the generated graph. HTML5 seems capable. Status: proof-of-concept completed in 2020
[x] 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.
- See https://www.youtube.com/watch?v=RLKW7ZMJOf4 and https://flask.palletsprojects.com/en/3.0.x/testing/ which use PyTest
- See https://www.selenium.dev/selenium-ide/

Physics derivation graph: integration by parts

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