Create a fake label ref using list

Question

Hello everyone once again, after having resolved my doubt regarding the use of \label and \ref. Reading the comments, I have noticed that in many occasions do not need to use the referencing system, only the values associated with these.

My idea is not to use auxiliary files (need many files en some cases, append mode in .aux file no exist in TeX), save in memory list short answers to exercises , so when copying and pasting from one file to another not need to make major modifications (changue only a ref to list).

This is the file (which works)

% !file: test.tex
% arara: pdflatex
\documentclass{article}%
\usepackage{amsmath}
\usepackage{multicol}
\usepackage{enumitem}
\usepackage{tcolorbox}
\tcbuselibrary{many}
\usepackage{pgffor}

% Set key for multicols in enumitem
\SetEnumitemKey{columns}{before=\begin{multicols}{#1},after=\end{multicols}}%

% Some definition
\newtheorem{theorem}{Theorem}
\newtheorem{exercise}[theorem]{Exercise}

% from https://tex.stackexchange.com/a/215571/7832
\ExplSyntaxOn
\NewDocumentCommand{\storedata}{mm}
  {
   \bcp_store_data:nn { #1 } { #2 }
  }

\NewDocumentCommand{\appenddata}{mm}
 {
  \bcp_append_data:nn { #1 } { #2 }
 }

\DeclareExpandableDocumentCommand{\getdata}{O{1}m}
 {
  \bcp_get_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \bcp_store_data:nn #1 #2
 {
  % create the sequence if it doesn't exist or clear it if it exists
  \seq_if_exist:cTF { l_bcp_data_#1_seq }
   { \seq_new:c { l_bcp_data_#1_seq } }
   { \seq_clear:c { l_bcp_data_#1_seq } }
  % append the items
  \__bcp_append_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \bcp_append_data:nn #1 #2
 {
  % create the sequence if it doesn't exist, do nothing if it exists
  \seq_if_exist:cF { l_bcp_data_#1_seq }
   { \seq_new:c { l_bcp_data_#1_seq } }
  % append the items
  \__bcp_append_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \__bcp_append_data:nn #1 #2
 {
  % append items one at a time
  \tl_map_inline:nn { #2 }
   {
    \seq_put_right:cn { l_bcp_data_#1_seq } { ##1 }
   }
 }

\cs_new:Npn \bcp_get_data:nn #1 #2
 {
  % retrieve the requested item
  \seq_item:cn { l_bcp_data_#2_seq } { #1 }
 }
\ExplSyntaxOff

\begin{document}
\section{Exercices}

\begin{exercise}
Factoring next expression:
\end{exercise}

\begin{enumerate}
\item $a^{2}-b^{2}$
\item $x^{2}-2x+1$ 
\item $3x+3y+3z$
\item $3x+3y-6z$
\end{enumerate}
% save in list exe:1
\appenddata{exe:1}{{$\left(a-b\right)\left(a+b\right)$}}
\appenddata{exe:1}{{$\left(x-1\right)^{2}$}}
\appenddata{exe:1}{{$3x+3y+3z$}}
\appenddata{exe:1}{{$3\left(x+y-2z\right)$}}

\begin{exercise}
Solve:
\end{exercise}
\begin{enumerate}
\item $2x+3=5$
\item $5x-2=7$
\item $4-3x=5$
\end{enumerate}

% save in list exe:2
\appenddata{exe:2}{{$1$}}
\appenddata{exe:2}{{$\dfrac{9}{5}$}}
\appenddata{exe:2}{{$-\dfrac{1}{3}$}}

\section{Answer}
% #1 : pass to tcolorbox
% #2 : name
% #3 : list
% #4 : maxvalue
% #5 : columns
\DeclareTotalTColorBox{\answer}{O{} m m m O{4}}
{ colback=white,size=small,top=0mm,bottom=1.5mm, left=0mm,width=\columnwidth,title filled,%
  fontupper=\small,fonttitle=\small\sffamily,%
    adjusted title={#2},center title,#1}
  {% 
  \begin{enumerate}[columns=#5,leftmargin=15pt,labelsep=3pt,font=\footnotesize,nosep,widest=25,]%
  \small
  \setlength{\columnsep}{0pt} 
   \foreach \x in {1,...,#4} {
    \item \getdata[\x]{#3}%
    }
  \end{enumerate}
  }%
\answer{Exercise 1}{exe:1}{4}
\answer{Exercise 2}{exe:2}{3}[3]
\end{document}

Now comes my problem, the macro I take from Storing an array of strings in a command only works in local mode, if write it inside an environment it only exists in this and not outside it, that is, I will not be able to access it outside the environment. For example:

% save list in enumerate 
\begin{enumerate}
\item $a^{2}-b^{2}$ \appenddata{exe:1}{{$\left(a-b\right)\left(a+b\right)$}}
\item $x^{2}-2x+1$ \appenddata{exe:1}{{$\left(x-1\right)^{2}$}}
\item $3x+3y+3z$ \appenddata{exe:1}{{$3x+3y+3z$}}
\item $3x+3y-6z$ \appenddata{exe:1}{{$3\left(x+y-2z\right)$}}
\end{enumerate}

And my idea is that it works within enumerate environments, and then access values outside of them. I have tried with this:

% !file: test.tex
% arara: pdflatex
\documentclass{article}%
\usepackage{amsmath}
\usepackage{multicol}
\usepackage{enumitem}
\usepackage{tcolorbox}
\tcbuselibrary{many}
\usepackage{pgffor}

% Set key for multicols in enumitem
\SetEnumitemKey{columns}{before=\begin{multicols}{#1},after=\end{multicols}}%

% Some definition
\newtheorem{theorem}{Theorem}
\newtheorem{exercise}[theorem]{Exercise}

% from https://tex.stackexchange.com/a/215571/7832
\ExplSyntaxOn
\NewDocumentCommand{\storedata}{mm}
  {
   \bcp_store_data:nn { #1 } { #2 }
  }

\NewDocumentCommand{\appenddata}{mm}
 {
  \bcp_append_data:nn { #1 } { #2 }
 }

\DeclareExpandableDocumentCommand{\getdata}{O{1}m}
 {
  \bcp_get_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \bcp_store_data:nn #1 #2
 {
  % create the sequence if it doesn't exist or clear it if it exists
  \seq_if_exist:cTF { l_bcp_data_#1_seq }
   { \seq_new:c { l_bcp_data_#1_seq } }
   { \seq_clear:c { l_bcp_data_#1_seq } }
  % append the items
  \__bcp_append_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \bcp_append_data:nn #1 #2
 {
  % create the sequence if it doesn't exist, do nothing if it exists
  \seq_if_exist:cF { l_bcp_data_#1_seq }
   { \seq_new:c { l_bcp_data_#1_seq } }
  % append the items
  \__bcp_append_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \__bcp_append_data:nn #1 #2
 {
  % append items one at a time
  \tl_map_inline:nn { #2 }
   {
    \seq_put_right:cn { l_bcp_data_#1_seq } { ##1 }
   }
 }

\cs_new:Npn \bcp_get_data:nn #1 #2
 {
  % retrieve the requested item
  \seq_item:cn { l_bcp_data_#2_seq } { #1 }
 }
\ExplSyntaxOff

% Create a environment to encapsulate answer
\NewDocumentEnvironment{myenumerate}{m}{%
% Command to save answer
\NewDocumentCommand\sol{m}{%
    \appenddata{#1}{{##1}}% 
    }% close \sol
}%
{}% close myenumerate
\begin{document}
\section{Exercices}

\begin{exercise}
Factoring next expression:
\end{exercise}

\begin{myenumerate}{exe:1}
\begin{enumerate}
\item $a^{2}-b^{2}$ \sol{$\left(a-b\right)\left(a+b\right)$}
\item $x^{2}-2x+1$  \sol{$\left(x-1\right)^{2}$}
\item $3x+3y+3z$    \sol{$3x+3y+3z$}
\item $3x+3y-6z$    \sol{$3\left(x+y-2z\right)$}
\end{enumerate}
\end{myenumerate}

\begin{exercise}
Solve:
\end{exercise}

\begin{myenumerate}{exe:2}
\begin{enumerate}
\item $2x+3=5$ \sol{$1$}
\item $5x-2=7$ \sol{$\dfrac{9}{5}$}
\item $4-3x=5$ \sol{$-\dfrac{1}{3}$}
\end{enumerate}
\end{myenumerate}

\section{Answer}
% #1 : pass to tcolorbox
% #2 : name
% #3 : list
% #4 : maxvalue default: lenght of list
% #5 : columns
\DeclareTotalTColorBox{\answer}{O{} m m m O{4}}
{ colback=white,size=small,top=0mm,bottom=1.5mm, left=0mm,width=\columnwidth,title filled,%
  fontupper=\small,fonttitle=\small\sffamily,%
    adjusted title={#2},center title,#1}
  {% 
  \begin{enumerate}[columns=#5,leftmargin=15pt,labelsep=3pt,font=\footnotesize,nosep,widest=25,]%
  \small
  \setlength{\columnsep}{0pt} 
   \foreach \x in {1,...,#4} {
    \item \getdata[\x]{#3}%
    }
  \end{enumerate}
  }%
\answer{Exercise 1}{exe:1}{4}
\answer{Exercise 2}{exe:2}{3}[3]
\end{document}

Also try to add a key to enumitem to avoid writing a new environment

\SetEnumitemKey{reflist}{before=\storedata{#1}{}}%

But none of the options I tried worked out, so, here comes the big question: How do I modify \appendata|\storedata to make them work globally? \appendata would be like \label and \getdata would be as \ref, of course only with values and whitout .aux file (or two run).

Answer 1

In order to store the data globally, \seq_gput_right:Nn (and its variants) must be applied, otherwise the local saving gets lost ultimately after the group formed by the enumerate environment ends.

\seq_put_right:Nn however works only inside a group.

\documentclass{article}%
\usepackage{amsmath}
\usepackage{multicol}
\usepackage{enumitem}
\usepackage{tcolorbox}
\tcbuselibrary{many}
\usepackage{pgffor}

% Set key for multicols in enumitem
\SetEnumitemKey{columns}{before=\begin{multicols}{#1},after=\end{multicols}}%

% Some definition
\newtheorem{theorem}{Theorem}
\newtheorem{exercise}[theorem]{Exercise}

% from https://tex.stackexchange.com/a/215571/7832
\ExplSyntaxOn

% Reporter macro, is expandable
\cs_new:Npn \reportnumberofseqitems #1{%
 \seq_count:c {l_bcp_data_#1_seq}%
}


\NewDocumentCommand{\storedata}{mm}
  {
   \bcp_store_data:nn { #1 } { #2 }
  }

\NewDocumentCommand{\appenddata}{mm}
 {
  \bcp_append_data:nn { #1 } { #2 }
 }

\DeclareExpandableDocumentCommand{\getdata}{O{1}m}
 {
  \bcp_get_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \bcp_store_data:nn #1 #2
 {
  % create the sequence if it doesn't exist or clear it if it exists
  \seq_if_exist:cTF { l_bcp_data_#1_seq }
   { \seq_new:c { l_bcp_data_#1_seq } }
   { \seq_gclear:c { l_bcp_data_#1_seq } }
  % append the items
  \__bcp_append_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \bcp_append_data:nn #1 #2
 {
  % create the sequence if it doesn't exist, do nothing if it exists
  \seq_if_exist:cF { l_bcp_data_#1_seq }
   { \seq_new:c { l_bcp_data_#1_seq } }
  % append the items
  \__bcp_append_data:nn { #1 } { #2 }
 }

\cs_new_protected:Npn \__bcp_append_data:nn #1 #2
 {
  % append items one at a time
  \tl_map_inline:nn { #2 }
   {
    \seq_gput_right:cn { l_bcp_data_#1_seq } { ##1 }
   }
 }

\cs_new:Npn \bcp_get_data:nn #1 #2
 {
  % retrieve the requested item
  \seq_item:cn { l_bcp_data_#2_seq } { #1 }
 }
\ExplSyntaxOff

% Create a environment to encapsulate answer
\NewDocumentEnvironment{myenumerate}{m}{%
% Command to save answer
\NewDocumentCommand\sol{m}{%
    \appenddata{#1}{{##1}}% 
    }% close \sol
}%
{}% close myenumerate
\begin{document}
\section{Exercices}

\begin{exercise}
Factoring next expression:
\end{exercise}

\begin{myenumerate}{exe:1}
\begin{enumerate}
\item $a^{2}-b^{2}$ \sol{$\left(a-b\right)\left(a+b\right)$}
\item $x^{2}-2x+1$  \sol{$\left(x-1\right)^{2}$}
\item $3x+3y+3z$    \sol{$3x+3y+3z$}
\item $3x+3y-6z$    \sol{$3\left(x+y-2z\right)$}
\end{enumerate}
\end{myenumerate}

\begin{exercise}
Solve:
\end{exercise}

\begin{myenumerate}{exe:2}
\begin{enumerate}
\item $2x+3=5$ \sol{$1$}
\item $5x-2=7$ \sol{$\dfrac{9}{5}$}
\item $4-3x=5$ \sol{$-\dfrac{1}{3}$}
\end{enumerate}
\end{myenumerate}

There are \reportnumberofseqitems{exe:1} items in exe:1 and     \reportnumberofseqitems{exe:2} items in exe:2

\section{Answer}
% #1 : pass to tcolorbox
% #2 : name
% #3 : list
% #4 : maxvalue default: lenght of list
% #5 : columns
\DeclareTotalTColorBox{\answer}{O{} m m m O{4}}
{ colback=white,size=small,top=0mm,bottom=1.5mm, left=0mm,width=\columnwidth,title filled,%
  fontupper=\small,fonttitle=\small\sffamily,%
    adjusted title={#2},center title,#1}
  {% 
  \begin{enumerate}[columns=#5,leftmargin=15pt,labelsep=3pt,font=\footnotesize,nosep,widest=25,]%
  \small
  \setlength{\columnsep}{0pt} 
   \foreach \x in {1,...,#4} {
    \item \getdata[\x]{#3}%
    }
  \end{enumerate}
  }%
\answer{Exercise 1}{exe:1}{4}
\answer{Exercise 2}{exe:2}{3}[3]
\end{document}