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LSpice
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Reporting unconclusiveinconclusive experimental searches

In many areas of mathematics it is informative to conduct numerical experiments.

But, it not uncommon that the searches do not lead to the exemplesexamples or data one was hoping for. Since the numerical searches can be quite time consuming, it seems useful to share thesesthese negative results, so that others avoid spending time attempting the same searches.

What would be best practices in this regard? And would setting up and maintaining an open-access database be a realistic prospect?

As an example, consider the question of the (non-)existence of n$n$-body choreographies when allowing the bodies to have different masses and different time-lags (see this article of Montgomery"$n$-body choreographies" by Montgomery for background as of 2013, and Minton's fine applet for the type of numerical searches that one could try to adapt). I'd be interested to know what has been already attempted by others. I could ask experts, but it may well overlook work by other experts and by PhDPh.D. students.

Reporting unconclusive experimental searches

In many areas of mathematics it is informative to conduct numerical experiments.

But, it not uncommon that the searches do not lead to the exemples or data one was hoping for. Since the numerical searches can be quite time consuming, it seems useful to share theses negative results, so that others avoid spending time attempting the same searches.

What would be best practices in this regard? And would setting up and maintaining an open-access database be a realistic prospect?

As an example, consider the question of the (non-)existence of n-body choreographies when allowing the bodies to have different masses and different time-lags (see this article of Montgomery for background as of 2013, and Minton's fine applet for the type of numerical searches that one could try to adapt). I'd be interested to know what has been already attempted by others. I could ask experts, but it may well overlook work by other experts and by PhD students.

Reporting inconclusive experimental searches

In many areas of mathematics it is informative to conduct numerical experiments.

But, it not uncommon that the searches do not lead to the examples or data one was hoping for. Since the numerical searches can be quite time consuming, it seems useful to share these negative results, so that others avoid spending time attempting the same searches.

What would be best practices in this regard? And would setting up and maintaining an open-access database be a realistic prospect?

As an example, consider the question of the (non-)existence of $n$-body choreographies when allowing the bodies to have different masses and different time-lags (see "$n$-body choreographies" by Montgomery for background as of 2013, and Minton's fine applet for the type of numerical searches that one could try to adapt). I'd be interested to know what has been already attempted by others. I could ask experts, but it may well overlook work by other experts and by Ph.D. students.

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Thomas Sauvaget
Thomas Sauvaget
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Reporting unconclusive experimental searches

In many areas of mathematics it is informative to conduct numerical experiments.

But, it not uncommon that the searches do not lead to the exemples or data one was hoping for. Since the numerical searches can be quite time consuming, it seems useful to share theses negative results, so that others avoid spending time attempting the same searches.

What would be best practices in this regard? And would setting up and maintaining an open-access database be a realistic prospect?

As an example, consider the question of the (non-)existence of n-body choreographies when allowing the bodies to have different masses and different time-lags (see this article of Montgomery for background as of 2013, and Minton's fine applet for the type of numerical searches that one could try to adapt). I'd be interested to know what has been already attempted by others. I could ask experts, but it may well overlook work by other experts and by PhD students.