While I don't disagree with your definition of reproducibility, I want to point out that very few papers would satisfy that criteria, regardless of their use of a closed- vs open-source software.
Here is a recent example: Imperial College COVID-19 response team published an article[1] where they modeled different effects of non-pharmaceutical interventions, such as suppression and mitigation on the number of infected, deaths, etc. This is a very interesting result, but it's impossible to replicate their results in practice without contacting the authors, as their methodology is not enough to reproduce it.
While someone else[2] posted their own model that is very well documented and fully reproducible by anyone with a $230/year personal license.
While theoretically [1] is high science and [2] is not, in my own opinion [2] is better than [1]. I would love more science to be done and discussed that way. Ideally, using open-source software, but in practice, using Wolfram Language, in that case, is already good enough in my opinion.
PS. I'm not affiliated with Wolfram Research in any way.
Making an exact copy of an experiment is the lwest level of reproducibility.
In science , reproducibility means reproducing the results with different components (people, tools, methodology), showing robust Independence form potential confounders.
Here is a recent example: Imperial College COVID-19 response team published an article[1] where they modeled different effects of non-pharmaceutical interventions, such as suppression and mitigation on the number of infected, deaths, etc. This is a very interesting result, but it's impossible to replicate their results in practice without contacting the authors, as their methodology is not enough to reproduce it.
While someone else[2] posted their own model that is very well documented and fully reproducible by anyone with a $230/year personal license.
While theoretically [1] is high science and [2] is not, in my own opinion [2] is better than [1]. I would love more science to be done and discussed that way. Ideally, using open-source software, but in practice, using Wolfram Language, in that case, is already good enough in my opinion.
PS. I'm not affiliated with Wolfram Research in any way.
[1] https://www.imperial.ac.uk/media/imperial-college/medicine/s...
[2] https://community.wolfram.com/groups/-/m/t/1901002