This post documents the steps taken to get the derivations in the paper Speed of sound from fundamental physical constants into the Physics Derivation Graph.
1) Read the paper. I need to understand the point of the paper and where content is in the text.
2) Identify the primary result of the derivation. Which equation is the output? Is there more than one? In this paper, equation 1 is the primary result.
Tangent: I tested whether the most popular equation is the most important.
This is measurable using the command
cat sound1.tex | tr " " "\n" |\ # replace spaces with newlines -- word tokenization
grep "ref{" |\ # find internal references to labeled expressions
sed 's/.*\\ref{//' | sed 's/}.*//' |\ # remove the irrelevant latex "\ref{}" to isolate the expression label ID
sort | uniq -c | sort -n # rank the popularity of expression labels
2 v001
3 abinitio
3 all
3 ratio
3 v0
3 v01
3 v1
5 elemental
6 bohr
6 rydberg
11 a
15 v00
15 v3
Decoding those latex labels to equations in the PDF,
"v3" is equation 9, which is tied for most popular with "v00" -- equation 4. The second most popular label "a" is equation 10.
The equation I'm claiming as the primary result, equation 1, is labeled as "v0" and is referenced 3 times.
3) What sections of the paper contain the derivation?
There are actually two derivations of the same result.
- one derivation is on page 2 column 1
- another derivation is on page 2 column 2
4) Determine whether the derivation already exist in the Physics Derivation Graph database. Check
- https://derivationmap.net/list_all_expressions
- https://derivationmap.net/list_all_symbols
- https://derivationmap.net/list_all_derivations
5) On paper, write out equations from the paper. Here I'm limiting the scope to one derivation on page 2 column 1. Fill in additional equations that are missing from the text. Use arrows to denote flow of derivation.
Often I'll make math mistakes or go down paths that turn out to be irrelevant. If I were a typical researcher, this is where the reconstruction process would stop.
6) On a separate paper, rewrite the graph and label the edges in the directed graph to describe the operation being carried out.
7) On a separate paper, rewrite the content from the previous step to refine the "operation being carried out" to a directed graph with inference rules available in the Physics Derivation Graph.
8) Identify all symbols used in the derivation: \rho, V, x, a, m, \alpha, M, K, \hbar, c, \pi, \epsilon_0
9) Identify which symbols in the derivation already exist in the Physics Derivation Graph and which need to be added. Record the symbol ID of each for later use.
10) Add missing symbols into the the Physics Derivation Graph database using https://derivationmap.net/list_all_symbols#add%20symbol
11) Identify which inference rules the derivation uses.
12) Identify which inference rules for this derivation exist in the Physics Derivation Graph and which need to be added.
13) If novel inference rules are needed for this derivation, enter those in https://derivationmap.net/list_all_inference_rules#add_inf_rule
14) Using https://derivationmap.net/start_new_derivation/, enter the expressions and inference rules for the steps of the derivation. For each step,
- ensure the symbols are referenced correctly in each expression
- ensure the SymPy version of the expression is correct
The output of this step is https://derivationmap.net/review_derivation/608598/
15) Offline, in the JSON file containing the derivation, edit the symbol IDs and SymPy representations as needed to get the step validations to be correct.
Review the modifications on https://derivationmap.net/review_derivation/608598/
TODO: The extensive linking of variables to definitions is not made accessible in the output, so there is no way for the user to leverage the linked information.
- expressions in the PDF/HTML output contain variables which have no link to their definitions
- variables in the text of the PDF/HTML output are not linked to the expressions or their definitions
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