Annotated bibliography: two bibliographies, one bib file

Question

I'm working on an annotated bibliography project. I have one bib file and need two bibliographies: one sorted chronologically, and the other sorted alphabetically. I want both bibliographies to include all the bib entries in my bib file. Moreover, in the bib file, each entry has a NOTE field which contains a summary of the paper/book. In the chronological bibliography, the NOTE fields are printed, but I don't want to have them twice and so they are not printed in the alphabetical bibliography. I am only allowed to use biblatex (not bibtex, amsrefs, etc.) due to other restrictions on the project. (EDIT: it seems we can use other fields other than NOTE [such as ANNOTE] for writing the summaries.)

I have two problems:

1. I don't know how to manage the labels for the alphabetical bibliography. I've used labelprefix=A to get reference labels like [A1] to avoid confusion with labels like [1] in the first bibliography. However, this causes a funny situation. In the NOTE field of the entries in the first bibliography, we list the cited papers in the entry. We want to see something like [2, 4], but now it looks like [A2, 4] (this is only happening to some of the references), see the image. Another solution would be to have the labels of the second bibliography be numbers, but each entry gets the same number as in the first bibliography. This way, there is one reference number for each entry and there will be no problem. I saw some examples for handling similar situations with refsection or refsegment but I couldn't make it work. Any help/suggestions would be appreciated.

2. I have manually defined a \myspace command to make the spacing in the NOTE field look pretty in the output. In particular, I have used this command at the beginning of the NOTE field for all the entries. Also, some of the notes which are longer have been split into paragraphs and \myspace is put between any two paragraphs. Is there any way to do this automatically (or in a more professional way)?

MWE:

ABCPNT.tex:

\documentclass{amsart}
\usepackage{blindtext}
\usepackage[sorting=ynt, backend=biber, datamodel=mrnumber, style=numeric-comp, sortcites]{biblatex}
\usepackage[colorlinks=true, pdfstartview=FitH, linkcolor=blue,
citecolor=blue, urlcolor=blue]{hyperref}

\addbibresource{ABCPNT.bib}  % File given below
\setlength\bibitemsep{0.2cm} % Space between references
\newcommand{\myspace}{\vspace*{0.3cm}\newline} % Space before/inside the NOTE field
\newbool{killnote} \AtEveryBibitem{\ifbool{killnote}{\clearfield{note}}{}} % To suppress the NOTE field in the second bibliography

\begin{document}
\nocite{*} % Include all the bib entries in bibliographies

\section{Chronological bibliography}
\printbibliography[heading=none] % The first bibliography, sorted by year

\section{Alphabetic bibliography}
\newrefcontext[sorting=nyt, labelprefix=A] % Change the sorting to name-year-title, adding a prefix A to the label of all entries
\booltrue{killnote} % Do not print the NOTE field in bib entires
\printbibliography[heading=none] % The second bibliography, sorted alphabetically
\end{document}

ABCPNT.bib

@article {ref1,
    AUTHOR = {Chebyshev, P.},
    TITLE = {{Lettre de M. le professeur Tchebychev a M. Fuss, sur un nouveau th{e}oreme relatif aux nombres premiers contenus dans la formes $4n+1$ et $4n+3$.}},
    FJOURNAL = {Bull. de la Classe phys. math. de l'Acad. Imp. des Sciences St. Petersburg},
    VOLUME = {11},
    YEAR = {1853},
    LANGUAGE = {French},
    NOTE = {\myspace Chebyshev's paper which was the starting point of the subject.},
}
%%%-------------------------------------------------------------------------------
@article{ref2,
    AUTHOR = {Phragmen, P.},
    TITLE = {{Sur le logarithme integral et la fonction $f(x)$ de Riemann}},
    YEAR  = {1891},
    FJOURNAL = {\"{O}fversigt af Kongl. Vetenskaps--Akademiens F\"{o}handlingar.},
    LANGUAGE = {French},
    VOLUME = {48},
    NOTE = {\myspace \blindtext \myspace This article cites~\cites{ref4, ref5}.},
}
%%%-------------------------------------------------------------------------------
@article{ref3,
    AUTHOR = {Landau, E.},
    TITLE = {{U}ber einen {S}atz von {T}schebyschef},
    JOURNAL = {Math. Ann.},
    FJOURNAL = {Mathematische Annalen},
    VOLUME = {61},
    YEAR = {1906},
    NUMBER = {4},
}
%%%-------------------------------------------------------------------------------
@article{ref4,
    author={Littlewood, J. E. },
    title={{Sur la distribution des nombres premiers}},
    year={1914},
    volume={158},
    journal={Comptes Rendus de l'Acad. Sci. Paris},
    language={French},
    note = {\myspace This article cites~\cites{ref4, ref5}.}
    }
%%%-------------------------------------------------------------------------------
@article{ref5,
    author={Hardy, G. H. and Littlewood, J. E. },
    title={{Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes}},
    year={1916},
    journal={Acta Math.},
    volume={41},
    number={1},
    note = {\myspace This article cites~\cites{ref1, ref4, ref3}.},
}

Answer 1

Since fields other than note are acceptable I suggest you use annotation instead. By default that field is not printed by most standard styles, but we can quickly change that.

As discussed in https://github.com/plk/biblatex/issues/904 the situation with the citations in the bibliography is a bit tricky. Usually I recommend not to use \cite in the bibliography to avoid these sort of issues. An explicit refcontext assignment (see MWE below \assignrefcontextentries) as suggested by PLK might help here.

The initial \myspace can be made redundant by issuing a \par (wrapped in \setunit) before printing the field contents. Within the field contents new paragraphs should be started with \par, using blank lines as usual in the rest of a .tex document will unfortunately not work. See Multiple paragraphs in bibliography fields via double line breaks and Preserve line breaks/newlines when parsing bib file with biber.

The redefinition of the bibliography environment was needed to be able to control the \parindent with \bibparindent.

\documentclass{amsart}
\usepackage{blindtext}
\usepackage[sorting=ynt, backend=biber, style=numeric-comp]{biblatex}
\usepackage{hyperref}

\assignrefcontextentries*[sorting=nyt, labelprefix=A]{*}

\newtoggle{showannotation}
\toggletrue{showannotation}

\renewbibmacro*{finentry}{%
  \iftoggle{showannotation}
    {\setunit{\par}%
     \printfield{annotation}}
    {}%
  \finentry}

\setlength{\bibitemsep}{.5\baselineskip}
\setlength{\bibparsep}{.5\bibitemsep}

\newlength{\bibparindent}
\setlength{\bibparindent}{0pt}

\defbibenvironment{bibliography}
  {\list
     {\printtext[labelnumberwidth]{%
        \printfield{labelprefix}%
        \printfield{labelnumber}}}
     {\setlength{\labelwidth}{\labelnumberwidth}%
      \setlength{\leftmargin}{\labelwidth}%
      \setlength{\labelsep}{\biblabelsep}%
      \addtolength{\leftmargin}{\labelsep}%
      \setlength{\itemsep}{\bibitemsep}%
      \setlength{\parsep}{\bibparsep}%
      \setlength{\listparindent}{\bibparindent}}%
      \renewcommand*{\makelabel}[1]{\hss##1}}
  {\endlist}
  {\item}

\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article {ref1,
    AUTHOR = {Chebyshev, P.},
    TITLE = {{Lettre de M. le professeur Tchebychev a M. Fuss, sur un nouveau th{e}oreme relatif aux nombres premiers contenus dans la formes $4n+1$ et $4n+3$.}},
    FJOURNAL = {Bull. de la Classe phys. math. de l'Acad. Imp. des Sciences St. Petersburg},
    VOLUME = {11},
    YEAR = {1853},
    LANGUAGE = {french},
    annotation = {Chebyshev's paper which was the starting point of the subject.},
}
@article{ref2,
    AUTHOR = {Phragmen, P.},
    TITLE = {{Sur le logarithme integral et la fonction $f(x)$ de Riemann}},
    YEAR  = {1891},
    FJOURNAL = {\"{O}fversigt af Kongl. Vetenskaps--Akademiens F\"{o}handlingar.},
    LANGUAGE = {French},
    VOLUME = {48},
    annotation = {\blindtext \par This article cites~\cite{ref4, ref5}.},
}
@article{ref3,
    AUTHOR = {Landau, E.},
    TITLE = {{U}ber einen {S}atz von {T}schebyschef},
    JOURNAL = {Math. Ann.},
    FJOURNAL = {Mathematische Annalen},
    VOLUME = {61},
    YEAR = {1906},
    NUMBER = {4},
}
@article{ref4,
    author={Littlewood, J. E. },
    title={{Sur la distribution des nombres premiers}},
    year={1914},
    volume={158},
    journal={Comptes Rendus de l'Acad. Sci. Paris},
    language={French},
    annotation = {This article cites~\cite{ref4, ref5}.}
}
@article{ref5,
    author={Hardy, G. H. and Littlewood, J. E. },
    title={{Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes}},
    year={1916},
    journal={Acta Math.},
    volume={41},
    number={1},
    annotation = {This article cites~\cite{ref1, ref4, ref3}.},
}
\end{filecontents}
\addbibresource{\jobname.bib}

\begin{document}
\nocite{*}

\section{Chronological bibliography}
\printbibliography[heading=none]

\section{Alphabetic bibliography}
\togglefalse{showannotation}
\newrefcontext[sorting=nyt, labelprefix=A] 
\printbibliography[heading=none]
\end{document}