A crowdsourced repository for optimization constants?

Thomas Bloom’s Erdös problem site has become a real hotbed of activity in recent months, particularly as some of the easiest of the outstanding open problems have turned out to be amenable to various AI-assisted approaches; there is now a lively community in which human contributions, AI contributions, and hybrid contributions are presented, discussed, and in some cases approved as updates to the site.

One of the lessons I draw from this is that once a well curated database of precise mathematical problems is maintained, it becomes possible for other parties to build upon it in many ways (including both AI-based and human-based approaches), to systematically make progress on some fraction of the problems.

This makes me wonder what other mathematical databases could be created to stimulate similar activity. One candidate that came to mind are “optimization constants” – constants that arise from some mathematical optimization problem of interest, for instance finding the best constant for which a certain functional inequality is satisfied.

I am therefore proposing to create a crowdsourced repository for such constants, to record the best upper and lower bounds known for any given such constant, in order to help encourage efforts (whether they be by professional mathematicians, amateur mathematicians, or research groups at a tech company) to try to improve upon the state of the art.

There are of course thousands of such constants one could consider, but just to set the discussion going, I set up a very minimal, proof of concept Github repository holding over 20 constants including:

1. , the constant in a certain autocorrelation quantity relating to Sidon sets. (This constant seems to have a surprisingly nasty optimizer; see this tweet thread of Damek Davis.)
2. , the constant in Erdös’ minimum overlap problem.

Here, I am taking inspiration from the Erdös problem web site and arbitrarily assigning a number to each constant, for ease of reference.

Even in this minimal state I think the repository is ready to start accepting more contributions, in the form of pull requests that add new constants, or improve the known bounds on existing constants. (I am particularly interested in constants that have an extensive literature of incremental improvements in the lower and upper bounds, and which look at least somewhat amenable to computational or AI-assisted approaches.) But I would be interested to hear feedback on how to improve the repository in other ways.