Appending Data to Bibliography with Biblatex

Question

I am trying to add a custom 'field' to my bibtex data, and then call that. However, I am getting a very strange scenario: when I call the field mr, then it works; when I call it mrnumber, then it doesn't work. Below is a MWE.

\documentclass[]{article}

\usepackage{filecontents}
\begin{filecontents*}{ext-eprint.dbx}
\ProvidesFile{ext-eprint.dbx}[2016/09/11 extended stand-alone eprint fields]
\DeclareDatamodelFields[type=field,datatype=verbatim]{arxiv,mr}
\DeclareDatamodelEntryfields{arxiv,mr}
\end{filecontents*}

\begin{filecontents*}{\jobname.bib}
@article{AGHH:dynamic-cm,
    archivePrefix = {arXiv},
    eprinttype = {arxiv},
    eprint = {1606.07639},
    title = {Mixing Times of Random Walks on Dynamic Configuration Models},
    date = {2016-06-24},
    author = {Avena, Luca and G{\"u}lda{\c s}, Hakan and van der Hofstad, Remco and den Hollander, Frank},
    options = {useprefix=true}
}
@article{FR:giant-mixing,
    title = {The Evolution of the Mixing Rate of a Simple Random Walk on the Giant Component of a Random Graph},
    volume = {33},
    number = {1},
    journaltitle = {Random Structures \& Algorithms},
    urldate = {2018-03-22},
    date = {2008-05-12},
    pages = {68-86},
    author = {Fountoulakis, Nikolaos and Reed, Bruce A.},
    mr = {12}
}
@book{LPW:markov-mixing,
    location = {{Providence, RI, USA}},
    title = {Markov {{Chains}} and {{Mixing Times}}},
    isbn = {978-1-4704-2962-1},
    pagetotal = {xvi+447},
    publisher = {{American Mathematical Society}},
    date = {2017},
    author = {Levin, David A. and Peres, Yuval and Wilmer, Elizabeth L.},
    mr = {3726904},
}
\end{filecontents*}

\usepackage{csquotes}
\usepackage[doi=false,isbn=false,url=false,
    backend=biber,
    style=numeric,
    datamodel=ext-eprint]{biblatex}
\usepackage{hyperref}
\addbibresource{\jobname.bib}

\makeatletter
\DeclareFieldFormat{arxiv}{%
    ---HOW DO I CUSTOMISE THIS??---}%\href{https://arxiv.org/abs/#1}}
\makeatother
\DeclareFieldFormat{mr}{%
    {\href{http://www.ams.org/mathscinet-getitem?mr=MR#1}{MR#1}}}

\renewbibmacro*{eprint}{%
  \printfield{arxiv}%
  \newunit\newblock
  \printfield{mr}%
  \newunit\newblock
  \iffieldundef{eprinttype}
    {\printfield{eprint}}
    {thisdoesappear\printfield[eprint:\strfield{eprinttype}]{eprint}}
}


\begin{document}
  \nocite{*}
  \printbibliography
\end{document}

This prints out the following.

However, if I replace all five references to mr with mrnumber, then I get the same output just without the MR3726904 appended. I got the majority of the structure from moewe's answer to BibTeX fields for DOI, MR, Zbl and arxiv?.

As you may have noticed in the MWE, I do \DeclareFieldFormat{arxiv}{..., but whatever I put in here does not affect the output, only the thisdoesappear appears, and this is in an \iffieldundef statement. I do want to just use eprint for both arXiv and MR, because each item will have precisely one of these. I'd like to be able to customise the appearance of the arxiv part, as I have done with the MR part.

Remark. I know some of the other formatting isn't very nice, but don't worry about that: I've looked at that separately, and have just tried to put the minimal amount in for the example here.

Answer 1

There are several things going on here. The most important thing is that biblatex distinguishes the explicitly defined arxiv and mrnumber field from the eprint field. The eprint field is special and its contents get special treatment.

1. In the MWE below mrnumber works for me. The code is just a result of replacing all mrs in your code with mrnumber.
2. If you want to change the output of arXiv-eprints, you don't modify the field format arxiv, you need to modify eprint:arxiv. You can see that eprint:arxiv is used by examining the false branch of iffieldundef{eprinttype}: \printfield[eprint:\strfield{eprinttype}]{eprint}. This calls the field format eprint:<eprinttype>, so eprint:arxiv in our case. \DeclareFieldFormat{arxiv} works only if you use the arxiv field directly.
3. You could also use eprint for both arXiv and mrnumber, but then you would have to transform mrnumber to eprints. This could be done automatically with a sourcemap. The advantage of that approach is that you don't need a new .dbx file. The disadvantage is that the mrnumber occupies the eprint slot.

The code below shows three ways to deal with MR numbers and arXiv links

1. Write the identifier into the eprint field and the type (arxiv, mrnumber) into eprinttype manually. See entries AGHH:dynamic-cm and FR:giant-mixing.
2. Use a dedicated arxiv and mrnumber field in the source. This is what baez/online and LPW:markov-mixing do. The implementation on the biblatex side can be done in two ways here.
   1. Internally re-map arxiv = {foo} to eprint = {foo} with eprinttype = {arxiv} and mrnumber = {bar} to eprint = {bar} with eprinttype = {mrnumber}. This is done with the out-\iffalsed source map below, the data model is not needed in that case. This results in the fields being treated just like eprint, which means DeclareFieldFormat{eprint:arxiv} and DeclareFieldFormat{eprint:mrnumber} are the formats responsible, the fields are printed with \printfield[eprint:\strfield{eprinttype}]{eprint}. The advantage of this approach is that you don't need a data model, the disadvantage is that the one eprint slot you have is occupied. On the biblatex side (i.e. for writing a biblatex style) this is equivalent to the first method.
   2. Declare the arxiv and mrnumber fields as native fields in a special data model and load the data model. The fields can be used independently and are controlled with DeclareFieldFormat{arxiv} and DeclareFieldFormat{mrnumber} and printed with \printfield{arxiv} and \printfield{mrnumber}.

\documentclass{article}

\usepackage{filecontents}
\begin{filecontents*}{ext-eprint.dbx}
\ProvidesFile{ext-eprint.dbx}[2018/05/09 extended stand-alone eprint fields]
\DeclareDatamodelFields[type=field,datatype=verbatim]{arxiv,mrnumber}
\DeclareDatamodelEntryfields{arxiv,mrnumber}
\end{filecontents*}

\begin{filecontents*}{\jobname.bib}
@online{AGHH:dynamic-cm,
  eprinttype    = {arxiv},
  eprint        = {1606.07639},
  title         = {Mixing Times of Random Walks on Dynamic Configuration Models},
  date          = {2016-06-24},
  author        = {Avena, Luca and G{\"u}lda{\c s}, Hakan and van der Hofstad, Remco and den Hollander, Frank},
  options       = {useprefix=true}
}
@online{baez/online,
  author  = {Baez, John C. and Lauda, Aaron D.},
  title   = {Higher-Dimensional Algebra {V}: 2-Groups},
  date    = {2004-10-27},
  version = 3,
  arxiv   = {math/0307200v3},
}
@article{FR:giant-mixing,
  title        = {The Evolution of the Mixing Rate of a Simple Random Walk on the Giant Component of a Random Graph},
  volume       = {33},
  number       = {1},
  journaltitle = {Random Structures \& Algorithms},
  urldate      = {2018-03-22},
  date         = {2008-05-12},
  pages        = {68-86},
  author       = {Fountoulakis, Nikolaos and Reed, Bruce A.},
  eprinttype   = {mrnumber},
  eprint       = {12},
}
@book{LPW:markov-mixing,
  location  = {Providence, RI, USA},
  title     = {Markov Chains and Mixing Times},
  isbn      = {978-1-4704-2962-1},
  pagetotal = {xvi+447},
  publisher = {American Mathematical Societ},
  date      = {2017},
  author    = {Levin, David A. and Peres, Yuval and Wilmer, Elizabeth L.},
  mrnumber  = {3726904},
}
\end{filecontents*}

\usepackage{csquotes}
\usepackage[doi=false,isbn=false,url=false,
  backend=biber,
  style=numeric,
  datamodel=ext-eprint, % comment this out to see what the data model does
]{biblatex}
\usepackage{hyperref}
\addbibresource{\jobname.bib}

\DeclareFieldFormat{arxiv}{%
  arXiv\addcolon\space
    \ifhyperref
      {\href{https://arxiv.org/abs/#1}{\nolinkurl{#1}}}
      {\nolinkurl{#1}}%
  \addspace
  as field}
\DeclareFieldFormat{eprint:arxiv}{%
  arXiv\addcolon\space
    \ifhyperref
      {\href{https://arxiv.org/abs/#1}{\nolinkurl{#1}}}
      {\nolinkurl{#1}}%
  \addspace
  via eprint}

\DeclareFieldFormat{mrnumber}{%
  \ifhyperref
    {\href{http://www.ams.org/mathscinet-getitem?mr=MR#1}{MR#1}}
    {MR#1}%
  \addspace
  real field}
\DeclareFieldFormat{eprint:mrnumber}{%
  \ifhyperref
    {\href{http://www.ams.org/mathscinet-getitem?mr=MR#1}{MR#1}}
    {MR#1}%
  \addspace
  eprint}

% This map maps all mrnumber fields to eprints with eprinttype mrnumber
% and all arxiv fields to eprint with eprinttype arxiv
% If you remove the \iffalse and \fi, this becomes active,
% in that case the datamodel is not needed any more.
\iffalse
\DeclareSourcemap{
  \maps[datatype=bibtex]{
    \map{
      \step[fieldsource=mrnumber, fieldtarget=eprint, final]
      \step[fieldset=eprinttype, fieldvalue=mrnumber]
    }
    \map{
      \step[fieldsource=arxiv, fieldtarget=eprint, final]
      \step[fieldset=eprinttype, fieldvalue=arxiv]
    }
  }
}
\fi

\renewbibmacro*{eprint}{%
  \printfield{arxiv}%
  \newunit\newblock
  \printfield{mrnumber}%
  \newunit\newblock
  \iffieldundef{eprinttype}
    {\printfield{eprint}}
    {\printfield[eprint:\strfield{eprinttype}]{eprint}}}

\begin{document}
  \nocite{*}
  \printbibliography
\end{document}

Answer 2

This is a suggestion for you to use the easily extensible eprint facilities of biblatex (moewe's third suggestion).

For that, you have to create a field format for your desired new eprint in the format biblatex expects. In your case eprint:mr:

\DeclareFieldFormat{eprint:mr}{% based on eprint:jstor
  \autocap{a}vailable\space at\space MR\addcolon\space
  \ifhyperref
    {\href{http://www.ams.org/mathscinet-getitem?mr=MR#1}{\nolinkurl{#1}}}
    {\nolinkurl{#1}}}

You can keep mrnumber and remap it to eprint with:

\DeclareSourcemap{
  \maps[datatype=bibtex]{
    \map{
      \step[fieldsource=mrnumber, fieldtarget=eprint, final]
      \step[fieldset=eprinttype, fieldvalue=mr]
    }
  }
}

This also sets eprinttype to mr for all entries which contain a mrnumber.

As to customizing arXiv, you should use \DeclareFieldFormat{eprint:arxiv}, as explained by moewe.

Putting things together:

\documentclass[]{article}

\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@article{AGHH:dynamic-cm,
    eprinttype = {arxiv},
    eprint = {1606.07639},
    title = {Mixing Times of Random Walks on Dynamic Configuration Models},
    date = {2016-06-24},
    author = {Avena, Luca and G{\"u}lda{\c s}, Hakan and van der Hofstad, Remco and den Hollander, Frank},
    options = {useprefix=true}
}
@article{FR:giant-mixing,
    title = {The Evolution of the Mixing Rate of a Simple Random Walk on the Giant Component of a Random Graph},
    volume = {33},
    number = {1},
    journaltitle = {Random Structures \& Algorithms},
    urldate = {2018-03-22},
    date = {2008-05-12},
    pages = {68-86},
    author = {Fountoulakis, Nikolaos and Reed, Bruce A.},
    mrnumber = {12}
}
@book{LPW:markov-mixing,
    location = {{Providence, RI, USA}},
    title = {Markov {{Chains}} and {{Mixing Times}}},
    isbn = {978-1-4704-2962-1},
    pagetotal = {xvi+447},
    publisher = {{American Mathematical Society}},
    date = {2017},
    author = {Levin, David A. and Peres, Yuval and Wilmer, Elizabeth L.},
    mrnumber = {3726904},
}
\end{filecontents*}

\usepackage{csquotes}
\usepackage[doi=false,isbn=false,url=false,
    backend=biber,
    style=numeric]{biblatex}
\usepackage{hyperref}
\addbibresource{\jobname.bib}

\DeclareSourcemap{
  \maps[datatype=bibtex]{
    \map{
      \step[fieldsource=mrnumber, fieldtarget=eprint, final]
      \step[fieldset=eprinttype, fieldvalue=mr]
    }
  }
}

\makeatletter
\DeclareFieldFormat{eprint:arxiv}{%
  \autocap{a}vailable\space at\space arXiv\addcolon\space% <- changed here, relative to the default definition
  \ifhyperref
    {\href{https://arxiv.org/\abx@arxivpath/#1}{%
       \nolinkurl{#1}%
       \iffieldundef{eprintclass}
         {}
         {\addspace\texttt{\mkbibbrackets{\thefield{eprintclass}}}}}}
    {\nolinkurl{#1}%
     \iffieldundef{eprintclass}
       {}
       {\addspace\texttt{\mkbibbrackets{\thefield{eprintclass}}}}}}
\makeatother

\DeclareFieldFormat{eprint:mr}{% based on eprint:jstor
  \autocap{a}vailable\space at\space MR\addcolon\space
  \ifhyperref
    {\href{http://www.ams.org/mathscinet-getitem?mr=MR#1}{\nolinkurl{#1}}}
    {\nolinkurl{#1}}}


\begin{document}
\nocite{*}
\printbibliography
\end{document}