@@ -106,7 +106,7 @@ A wide variety of concrete datasets has been developed.

Typically, each one is maintained in a separate ad hoc database (like a text file with one entry per line) or SQL databases.

A living survey of such databases can be found in \cite{Bercic:cmo:wiki, bercic:cmo:table}.

At the time of writing, it contains about a hundred datasets, ranging from small (up to $100$ objects) to very large ($\approx17\cdot10^9$ objects).

Similarly varied is the authorship: from one author producing several smaller datasets (Conder \cite{ConderCensuses:on}, Poto\v{c}nik \cite{PotocnikCensuses:on}, McKay \cite{McKayData:on}, Royle \cite{RoyleData:on}, Wanless \cite{WanlessData:on}), to FindStat \cite{findstat} ($69$ contributors), LMFDB \cite{lmfdb:on} ($100$ contributors) and the OEIS \cite{oeis} with thousands of contributors.

Similarly varied is the authorship: from one author producing several smaller datasets (Conder \cite{ConderCensuses:on}, Poto\v{c}nik \cite{PotocnikCensuses:on}, McKay \cite{McKayData:on}, Royle \cite{RoyleData:on}, Wanless \cite{WanlessData:on}), to FindStat \cite{findstat} ($69$ contributors), LMFDB \cite{lmfdb:on} ($100$ contributors) and the OEIS \cite{OEIS:on} with thousands of contributors.

The oldest such datasest is the online encyclopedia of integer sequences.

It is notable for collecting not only mathematical objects but also symbolic data for their semantics (such as defining equations and generating functions).

@@ -22,25 +22,25 @@ It will contribute to a new generation of researchers that consider Open Science

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We describe how \TheProject contributes to each expected impact listed in the work programme.

We describe how \TheProject contributes to each of the three expected impacts listed in the work programme.

\paragraph{Expected Impact: Integrating research and service development}

As most mathematical services are written by the mathematical community, \inparahighlight{mathematicians are already co-designing research and services in current practice}.

The expected impact of the \pn project is that we provide the infrastructure and in some cases funding to make that easier and make the results more sustainable.

The expected impact of the \pn project is that we provide the infrastructure and in some cases funding to make that easier and make the results more accessible, findable, interoperable, and sustainable.

By providing clients for widely used research systems (see \taskref{services}{I} and \taskref{services}{modelicaservice}), \inparahighlight{we make it substantially easier and cheaper for service developers to combine their implementation work with their traditional research}.

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\noindent\textbf{KPIs}: To test this expectation, we will brief the participants of the ``Summer of Math Data'' events (see \taskref{dissem}{outreachul}) to keep track of their development investments and outcomes in terms of data and service features.

\noindent\textbf{KPIs}: To test this expectation, we will brief the participants of the ``Summer of Math Data'' development workshops (see \taskref{dissem}{outreachul}) to keep track of their development investments and the outcomes achieved in terms of data and service features.

We will evaluate these tallies and conduct interviews with the participants of the events about how much time they save by using our user-oriented services as a basis for their extensions.

We expect that, even though the \pn framework will still be in prototypical state at the time of these two ``summers'', the participants will already break even early on and will, during the project run time, see substantial savings of time and effort while improving their services.

\paragraph{Expected Impact: Supporting the objectives of Open Science}

\inparahighlight{The \pn project was specifically conceived in order to support Open Science in the mathematical sciences}, and its objectives directly feed into the objectives of Open Science.

\inparahighlight{The \pn project was specifically conceived to support Open Science in the mathematical sciences}, and its objectives directly feed into the objectives of Open Science.

In particular, \TheProject develops the foundations of FAIR Mathematics, implements a service infrastructure for Open Data in mathematical sciences, and evaluates it on a representative family of datasets and services.

Thus, it enables enable scientific and industrial applications by \inparahighlight{enabling users to openly access/search/reuse/interoperate with mathematical data from all scientific disciplines and sectors}.

For a concrete example of the value of Open Science in mathematics, consider the Fibonacci sequence (given by the recurrence equation $f(n)=f(n-1)+f(n-2)$): while it was originally of mathematical interest to describe the (idealized) reproduction of rabbits, it was soon discovered that this sequence governs the number of petals in certain kinds of flowers and is connected with the meters of traditional Indian poetry.

It is one of about 300.000 sequences collected in the Online Encyclopedia of Integer sequences (OEIS)~\cite{oeis,Sloane:OEIS}, and transdisciplinary interpretations of OEIS sequences abound but are non-obvious to find systematically.

It is one of about 325.000 sequences collected in the Online Encyclopedia of Integer sequences (OEIS)~\cite{OEIS:on,Sloane:OEIS}, and transdisciplinary interpretations of OEIS sequences abound but are non-obvious to find systematically.

The \pn project will integrate the OEIS and similar datasets into the EOSC and thus support the systematic cross-linking to other sciences.