From my impression, the nearest equivalent would be an academics' text source repository. This could be a library of theoretical works personally owned (and almost certainly monographic rather than papers). It could be a set of commonly referenced canon texts spread across four or five libraries in their region that they consult. It could be the items above plus documentary series such as archives, cultural texts.
The objects manipulated, day to day, in conducting humanities research are texts; whether these are straight texts, or the meanings developed from physical records, or the meanings developed reflecting on terse problem statements.
In my experience, some scholars keep detailed notes, and others don't. I try and keep my notes and sources in a deep text searchable database with what meta-data I can cheaply acquire. There is no standard for keeping a repository, and the way in which a scholar learns to keep an adequate repository is idiosyncratic.
There isn't a disciplinary standard for keeping a repository, above and beyond "study skills" type courses which aren't mandatory or systematised. To evidence of the adequacy of the "experiment" equivalent scholars demonstrate their mastery over the relevant texts by providing evidence of firmly supportable readings through citation and footnoting, or by quality argument.