The Mathematical Research Data Initiative (MaRDI4NFDI) is part of Germany's National Research Data Infrastructure and operates a knowledge graph for the mathematics domain built on MediaWiki/Wikibase, covering publications, datasets, algorithms, software, and research workflows. This linked-data architecture provides strong FAIR alignment out of the box: persistent identifiers, structured metadata, open SPARQL access, and RDF-native interoperability.

Yet FAIR data is not the same as a FAIR Digital Object. FDOs add a machine-actionable operations layer: typed objects with well-defined, protocol-level access - enabling automated discovery and processing without domain-specific knowledge of the underlying system.

We present our work on exposing MaRDI4NFDI knowledge graph entities as FDOs using the Digital Object Interface Protocol (DOIP) as an external gateway layer. This embeds FAIRification into the infrastructure layer, reducing the need for repeated per-dataset annotation, and demonstrates how domain-specific research infrastructures can contribute machine-actionable objects to federated ecosystems.

We share design decisions, open challenges in FDO profile definition for mathematical objects, and lessons relevant to other knowledge graph infrastructures built on MediaWiki/Wikibase.

As the capabilities of computer devices have grown, so have their use as tools in scientific research. It is now possible to do wild and wonderful things by relying on computers computers to generate useful results in the support of both research goals, as well as complex analysis required to reach these goals. This is usually done by the use of bespoke research software developed for the specific use case, or repurposing software already tailor made for research, but in new and innovative ways. However, this also means that computer programs play a more central role in the defense of a thesis. As good science require a peer review of the results, the computer programs so central to new computational results must also be readily available to the reviewers. But quite often, thought is not spent on ensuring proper reproducibility of software research.
A naive approach to making computer software available is to only make the source code available to reviewers. However, this approach poses problems with regards to ease of use, and also with regards to reproducibility. It may not be the easiest thing to get running in the first place. This may just be due to the convoluted way the prerequisites are meant to be installed. Or it may require obscure versions of libraries, which may conflict with existing libraries on a referee's host system. This can result in unnecessary frustrations, or complete failures, in trying to reproduce software results.
MaRDI, the mathematical consortium of the NFDI, has developed the MaRDI Packaging System (MaPS) (https://arxiv.org/abs/2404.05563) to solve this specific problem. This project is heavily inspired by the work done in this direction, for similar motivations in different fields, by Flatpak for generic Linux software, and Valve for PC video games. We co-opt the same basic technology used to run (reproduce) decode old video games on modern systems, and reap similar rewards.
MaPS makes packaging, distributing, installing, and running software across computers as easy as possible. This guarantees reproducibility of results which heavily rely on software without the additional burden of trying to setup software while taking special care to retain reproducibility. MaPS has been extensively tested and used across science domains: Mathematics, Biology, Computer Science, and research at the intersection of Physics, Chemistry, and Machine Learning.
MaPS sets up a software container, which includes the entire software stack required for the project. The boundary of the container enforces a separation between the host computer and the packaged software, and therefore avoids any potential conflicts between software versions installed on a user's computer v/s the software versions included in the runtime. A two way window into the runtime is available, which can be used to provide variable input, as well as extract output from the runtime. In addition, the changes made in a runtime persist by default, but a runtime can still be reset to the state it was published in. This allows a researcher to become familiar with the packaged software using traditional interactive interfaces without having to care about creating an experimental environment.
Creating runtimes is likewise easy. MaPS does not assume familiarity with scripts, manifest files, or complicated declaration systems to define the contents of a runtime. MaPS aims to be maximally friendly by providing an interactive session into the runtime being constructed, so to allow for bespoke and handcrafted environments: to fit exactly the, need and cater to the expertise of the researcher. Using MaPS requires minimal extra training, reducing the data management overhead for scientists, allowing them to spend more time on research, and less time on perceived administrative tasks. Once the researcher is happy with the crafted runtime, it can be published on the official MaPS repository. Optionally, a private repository can be setup for uses like an internal repository for a lab, or a private repository to serve an event, like a conference repository for referees.
There are several methods for sharing a program for running on another machine ranging from sharing just the source code, to docker containers (via a dockerfile), or a full fat Virtual Machine (VM) disk image. We think MaPS is a superior option to these alternate methods. A MaPS runtime is more complete than just sharing source code, more light weight than sharing a VM, and more streamlined than running docker.
In conclusion, MaPS is a domain agnostic reproducible container toolkit which makes RDM goals with respect to software trivial to achieve, while trying to be as efficient with resources as possible. With no problems found in real world and synthetic testing, and multiple working proof of concepts, some of which successfully run 5 year old programs on modern computers without trouble, MaPS is the final word in long term software archiving for reproducibility.

I have designed the possibly first class of research data management for mathematicians and I have taught variations thereof as a semester long course and as one-day trainings at various CRCs and Graduiertenkollegs. I report on the content and lessons I learned myself. The lecture notes will be available in time with the DMV annual meeting under an open license.

Mechanism of quality control have been essential to establish trust in mathematical research for a long time, but until recently, they were predominantly employed to publications. Similar measures for research data are yet in their infancy, while at the same time tools powered by artificial intelligence offer hitherto unknown opportunities. We discuss some questions and approaches of the mathematical community to address these challenges, with a focus on what is currently provided by community platforms like zbMATH Open, and what might be necessary in the future.