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\begin{document}

\title[Spectral sequence data files]
{Data files for the algebraic Novikov, Adams, and Adams-Novikov
spectral sequences}

\author{Daniel C. Isaksen}
\address{
Department of Mathematics, 
Wayne State University, 
Detroit, MI 48202, USA}
\email{isaksen@wayne.edu}

\thanks{The first author was supported by NSF grant
DMS-1606290. The third author was supported by NSF grant DMS-1810638.
Many of the associated machine computations were performed on the
Wayne State University Grid high performance computing cluster.}

\author{Guozhen Wang}
\address{Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China, 200433}
\email{wangguozhen@fudan.edu.cn}

\author{Zhouli Xu}
\address{Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139}
\email{xuzhouli@mit.edu}

\subjclass[2010]{55T15, 55Q45, 14F42}

\keywords{algebraic Novikov spectral sequence, 
Adams spectral sequence, Adams-Novikov spectral sequence,
stable homotopy group,
motivic stable homotopy group, cohomology of the Steenrod algebra}

\begin{abstract}
This document describes the structure of some comma-separated-value
(CSV) files that contain detailed information about the algebraic
Novikov, Adams, and Adams-Novikov spectral sequences, in both the
classical and $\C$-motivic contexts.
\end{abstract}

\maketitle

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This document describes the structure of some comma-separated-value
(CSV) files that contain detailed information about the algebraic
Novikov, Adams, and Adams-Novikov spectral sequences, in both the
classical and $\C$-motivic contexts.
These files are auxiliary to the projects described in
\cite{IWX19b}, \cite{IWX19a}, \cite{IWX19c}, and \cite{IWX19d}.

See the cited documents for more mathematical details.
The remainder of this document describes the structure of the 
CSV files.

\newpage

\section{Classical Adams spectral sequence}

\file{Adams-classical-E2.csv:}
Each line of the file corresponds to an element in the
classical Adams $E_2$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{shift:} Used for display purposes
in reference to the chart in \cite{IWX19c},
when more than one element occurs with the same bidegree.
Lower values correspond to dots on the left.

\column{h0info:}
Information about special behavior of an $h_0$ extension. \\
\texttt{loc} means that an element is $h_0$-periodic. \\
\texttt{p} means that an $h_0$ extension is not known to occur.

\column{h0target:} Value of an $h_0$ extension.  An empty cell indicates
that there is no $h_0$ extension.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\column{drinfo:}
Information about an Adams differential.
An integer value $r$ indicates a $d_r$ differential. \\
\texttt{p} means that a differential is not known to occur.

\column{drtarget:}
Value of an Adams $d_r$ differential.

\newpage

\file{Adams-classical-Einfty.csv:}
Each line of the file corresponds to an element in the
classical Adams $E_\infty$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{shift:} Used for display purposes
in reference to the chart in \cite{IWX19c},
when more than one element occurs with the same bidegree.
Lower values correspond to dots on the left.

\column{h0info:}
Information about special behavior of an $h_0$ extension. \\
\texttt{loc} means that an element is $h_0$-periodic. \\
\texttt{h} means that there is a hidden $2$ extension. \\
\texttt{h ?} means that there is a possible hidden $2$ extension. \\
\texttt{p} means that an $h_0$ extension is not known to occur.

\column{h0target:} Value of an $h_0$ extension.  An empty cell indicates
that there is no $h_0$ extension.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
\texttt{h} means that there is a hidden $\eta$ extension. \\
\texttt{h ?} means that there is a possible hidden $\eta$ extension. \\
\texttt{p} means that the $h_1$ extension is not known to occur.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension.

\column{h2info:}
Information about special behavior of an $h_2$ extension. \\
\texttt{h} means that there is a hidden $\eta$ extension. \\
\texttt{p} means that the $h_1$ extension is not known to occur.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\column{drinfo:}
Information about an Adams differential.
An integer value $r$ indicates a $d_r$ differential. \\
\texttt{p} means that the differential is not known to occur.

\column{drtarget:}
Value of an Adams $d_r$ differential.

\newpage


\file{Adams-classical-Einfty-extn.csv:}
Each line of the file corresponds to a hidden extension by
$2$, $\eta$, or $\nu$ in the
classical Adams $E_\infty$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.

\column{source:}  Source of an extension.
(Beware that naming conventions have changed over time.)

\column{type:} Type of extension. \\
\texttt{h0} means an extension by $2$. \\
\texttt{h1} means an extension by $\eta$. \\
\texttt{h2} means an extension by $\nu$.

\column{stem:} The stem of the source of an extension.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
the source of an extension.  This is the vertical coordinate in a standard 
Adams chart.

\column{info:} Information about special behavior of an extension. \\
\texttt{?} means that an extension is not known to occur.

\column{target:} Target of an extension.

\column{sourcex, sourcey, targetx, targety}:
Used for display purposes in reference to the chart in \cite{IWX19c},
when a curved hidden extension is necessary.
Gives the tangent vectors at the source and target.

\newpage

\section{$\C$-motivic Adams spectral sequence}

\file{Adams-motivic-E2.csv:}
Each line of the file corresponds to an element in the
motivic Adams $E_2$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{tautorsion:} Indicates the $\tau$ module structure of an
element. \\
\texttt{0} means that an element is $\tau$-periodic. \\
Any other integer $k$ means that an element is annihilated by $\tau^k$.

\column{shift:} Used for display purposes
in reference to the chart in \cite{IWX19c},
when more than one element occurs with the same bidegree.
Lower values correspond to dots on the left.

\column{h0info:}
Information about special behavior of an $h_0$ extension. \\
\texttt{p} means that an $h_0$ extension is not known to occur.
\texttt{t} means that an $h_0$ extension equals $\tau$ times an element. \\
\texttt{t} followed by an integer $k$ means that an $h_0$ extension
equals $\tau^k$ times an element.

\column{h0target:} Value of an $h_0$ extension.  An empty cell indicates
that there is no $h_0$ extension. \\
\texttt{loc} means that an element is $h_0$-periodic.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
\texttt{p} means that an $h_1$ extension is not known to occur.
\texttt{t} means that an $h_1$ extension equals $\tau$ times an element. \\
\texttt{t} followed by an integer $k$ means that an $h_1$ extension
equals $\tau^k$ times an element.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension. \\
\texttt{loc} means that an element is $h_1$-periodic.

\column{h2info:}
Information about special behavior of an $h_2$ extension. \\
\texttt{p} means that an $h_2$ extension is not known to occur.
\texttt{t} means that an $h_2$ extension equals $\tau$ times an element. \\
\texttt{t} followed by an integer $k$ means that an $h_2$ extension
equals $\tau^k$ times an element.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\column{drinfo:}
Information about an Adams $d_2$ differential. \\
\texttt{free} means that the target of the differential is not displayed
on the chart, typically because it is $h_1$-periodic. \\
\texttt{p} means that a differential is not known to occur. \\
\texttt{t} means that a differential equals $\tau$ times an element. \\
\texttt{t} followed by an integer $k$ means that a differential
equals $\tau^k$ times an element.

\column{drtarget:}
Value of an Adams $d_2$ differential.

\newpage

\file{Adams-motivic-E3.csv:}
Each line of the file corresponds to an element in the
motivic Adams $E_3$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.
This file takes the same format as
\textbf{Adams-motivic-E2.csv}.


\file{Adams-motivic-E4.csv:}
Each line of the file corresponds to an element in the
motivic Adams $E_4$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.
This file takes the same format as
\textbf{Adams-motivic-E2.csv}.

\file{Adams-motivic-E5.csv:}
Each line of the file corresponds to an element in the
motivic Adams $E_5$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.
This file takes the same format as
\textbf{Adams-motivic-E2.csv}.

\file{Adams-motivic-E6.csv:}
Each line of the file corresponds to an element in the
motivic Adams $E_6$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.
This file takes the same format as
\textbf{Adams-motivic-E2.csv}.

\file{Adams-motivic-Einfty.csv:}
Each line of the file corresponds to an element in the
motivic Adams $E_\infty$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.
This file takes the same format as
\textbf{Adams-motivic-E2.csv}.

\newpage


\file{Adams-motivic-Einfty-extn.csv:}
Each line of the file corresponds to a hidden extension by
$\tau$ in the
$\C$-motivic Adams $E_\infty$-page.  This data is used to produce the
chart appearing in \cite{IWX19c}.

\column{source:}  Source of an extension.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of the source of an extension.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
the source of an extension.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{info:} Information about special behavior of an extension. \\
\texttt{?} means that an extension is not known to occur.

\column{target:} Target of an extension.

\column{sourcex, sourcey, targetx, targety}:
Used for display purposes in reference to the chart in \cite{IWX19c},
when a curved hidden extension is necessary.
Gives the tangent vectors at the source and target.

\newpage

\section{Adams-Novikov spectral sequence}

\file{ANSS-v1periodic-E2.csv:}
Each line of the file corresponds to a $v_1$-periodic element in the 
Adams-Novikov $E_2$-page.
This data is used to produce the chart appearing in
\cite{IWX19d}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.) 

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams-Novikov chart.

\column{Adams-Novikov filtration:} The Adams-Novikov filtration of 
an element.  This is the vertical coordinate in a standard 
Adams-Novikov chart.

\column{order:} $\log_2$ of the order of an element.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
\texttt{loc} means that an element is $h_1$-periodic.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\column{drinfo:}
Information about an Adams-Novikov differential. \\
An integer $r$ means that there is a $d_r$ differential.

\column{drtarget:}
Value of an Adams-Novikov differential.

\newpage

\file{ANSS-v1periodic-Einfty.csv:}
Each line of the file corresponds to a $v_1$-periodic element in the 
Adams-Novikov $E_\infty$-page.
This data is used to produce the chart appearing in
\cite{IWX19d}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.) 

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams-Novikov chart.

\column{Adams-Novikov filtration:} The Adams-Novikov filtration of 
an element.  This is the vertical coordinate in a standard 
Adams-Novikov chart.

\column{order:} $\log_2$ of the order of an element.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\newpage


\file{ANSS-v1periodic-Einfty-extn.csv:}
Each line of the file corresponds to a hidden extension
between $v_1$-periodic elements in the
Adams-Novikov $E_\infty$-page.  This data is used to produce the
chart appearing in \cite{IWX19d}.

\column{source:}  Source of an extension.
(Beware that naming conventions have changed over time.)

\column{type:} Type of extension. \\
\texttt{h0} means an extension by $2$. \\

\column{stem:} The stem of the source of an extension.  This is the
horizontal coordinate in a standard Adams-Novikov chart.

\column{Adams-Novikov filtration:} The Adams-Novikov filtration of 
the source of an extension.  This is the vertical coordinate in a standard 
Adams-Novikov chart.

\column{target:} Target of an extension.

\newpage

\file{ANSS-E2.csv:}
Each line of the file corresponds to an element in the
Adams-Novikov $E_2$-page, excluding $v_1$-periodic elements.
This data is used to produce the
chart appearing in \cite{IWX19d}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams-Novikov chart.

\column{Adams-Novikov filtration:} The Adams-Novikov filtration of 
an element.  This is the vertical coordinate in a standard 
Adams-Novikov chart.

\column{order:} $\log_2$ of the order of an element.

\column{shift:} Used for display purposes
in reference to the chart in \cite{IWX19d},
when more than one element occurs with the same bidegree.
Lower values correspond to dots on the left.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
An integer $k$ means that the $h_1$ extension equals
$2^k$ times a generator.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension.

\column{h2info:}
Information about special behavior of an $h_2$ extension. \\
An integer $k$ means that the $h_2$ extension equals
$2^k$ times a generator.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\column{drinfo:}
Information about an Adams-Novikov differential. \\
An integer $r$ means that there is a $d_r$-differential. \\
\texttt{?} means that a differential is not known to occur.

\column{drtarget:}
Value of an Adams-Novikov differential.

\newpage

\file{ANSS-E4.csv:}
Each line of the file corresponds to an element in the
Adams-Novikov $E_4$-page, excluding $v_1$-periodic elements.
This data is used to produce the
chart appearing in \cite{IWX19d}.
This file takes the same format as
\textbf{ANSS-E2.csv}.

\file{ANSS-E6.csv:}
Each line of the file corresponds to an element in the
Adams-Novikov $E_6$-page, excluding $v_1$-periodic elements.
This data is used to produce the
chart appearing in \cite{IWX19d}.
This file takes the same format as
\textbf{ANSS-E2.csv}.

\file{ANSS-Einfty.csv:}
Each line of the file corresponds to an element in the
Adams-Novikov $E_\infty$-page, excluding $v_1$-periodic elements.
This data is used to produce the
chart appearing in \cite{IWX19d}.
This file takes the same format as
\textbf{ANSS-E2.csv}.

\newpage

\file{ANSS-Einfty-extn.csv:}
Each line of the file corresponds to a hidden extension by
$2$, $\eta$, or $\nu$
in the Adams-Novikov $E_\infty$-page.  This data is used to produce the
chart appearing in \cite{IWX19d}.

\column{source:}  Source of an extension.
(Beware that naming conventions have changed over time.)

\column{type:} Type of extension. \\
\texttt{h0} means an extension by $2$. \\
\texttt{h1} means an extension by $\eta$. \\
\texttt{h2} means an extension by $\nu$.

\column{stem:} The stem of the source of an extension.  This is the
horizontal coordinate in a standard Adams-Novikov chart.

\column{Adams-Novikov filtration:} The Adams-Novikov filtration of 
the source of an extension.  This is the vertical coordinate in a standard 
Adams-Novikov chart.

\column{info:} Information about special behavior of an extension. \\
\texttt{?} means that an extension is not known to occur.

\column{target:} Target of an extension.

\column{sourcex, sourcey, targetx, targety}:
Used for display purposes in reference to the chart in \cite{IWX19d},
when a curved hidden extension is necessary.
Gives the tangent vectors at the source and target.

\newpage

\section{$h_1$-Bockstein spectral sequence for the 
algebraic Novikov $E_2$-page}

\file{algNovikov-h1periodic-E0.csv}
Each line of the file corresponds to an element in the
$E_0$-page of the 
$h_1$-Bockstein spectral sequence that converges to part of the
algebraic Novikov $E_2$-page.
This data is used to produce the chart appearing in
\cite{IWX19a}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{cell:} Indicates whether an element is detected by the top cell
or the bottom cell of the cofiber of $\tau$. \\
\texttt{0} means that an element is in the image in $\Ext$ 
of inclusion of the bottom cell.\\
\texttt{1} means that an element maps non-trivially in $\Ext$ 
under projection to the top cell.

\column{shift:} Used for display purposes
in reference to the chart in \cite{IWX19c},
when more than one element occurs with the same bidegree.
Lower values correspond to dots on the left.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
\texttt{?} means that an $h_1$ extension is not known to occur. \\
\texttt{h} means that an $h_1$ extension is hidden, in the sense
that its source is detected by the top cell of the cofiber of $\tau$,
while its target is detected by the bottom cell.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension. \\
\texttt{loc} means that an element is $h_1$-periodic.

\column{drinfo:}
Information about a Bockstein differential. \\
An integer $r$ means that there is a Bockstein $d_r$ differential. \\
\texttt{?} means that a differential is not known to occur.

\column{drtarget:}
Value of a Bockstein differential.

\newpage

\file{algNovikov-h1periodic-Einfty.csv}
Each line of the file corresponds to an element in the
$E_\infty$-page of the 
$h_1$-Bockstein spectral sequence that converges to part of the
algebraic Novikov $E_2$-page.
This data is used to produce the chart appearing in
\cite{IWX19a}.
This file takes the same format as
\textbf{algNovikov-h1periodic-E0.csv}.

\newpage

\section{Algebraic Novikov spectral sequence}

\file{algNovikov-E2.csv:}
Each line of the file corresponds to an element in the
algebraic Novikov $E_2$-page.
This data is used to produce the chart appearing in \cite{IWX19a}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{cell:} Indicates whether an element is detected by the top cell
or the bottom cell of the cofiber of $\tau$. \\
\texttt{0} means that an element is in the image in $\Ext$ of inclusion of the bottom cell.\\
\texttt{1} means that an element maps non-trivially in $\Ext$
under projection to the top cell.

\column{h0info:}
Information about special behavior of an $h_0$ extension. \\
\texttt{h} means that an $h_0$ extension is hidden, in the sense
that its source is detected by the top cell of the cofiber of $\tau$,
while its target is detected by the bottom cell.

\column{h0target:}
Value of an $h_0$ extension.  An empty cell indicates
that there is no $h_0$ extension. \\
\texttt{loc} means that an element is $h_0$-periodic.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
\texttt{?} means that an $h_1$ extension is not known to occur. \\
\texttt{h} means that an $h_1$ extension is hidden, in the sense
that its source is detected by the top cell of the cofiber of $\tau$,
while its target is detected by the bottom cell.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension. \\
\texttt{loc} means that an element is $h_1$-periodic.

\column{h2info:}
Information about special behavior of an $h_2$ extension. \\
\texttt{h} means that an $h_2$ extension is hidden, in the sense
that its source is detected by the top cell of the cofiber of $\tau$,
while its target is detected by the bottom cell.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension. 

\column{drinfo:}
Information about an algebraic Novikov differential. \\
An integer $r$ means that there is $d_r$ differential. \\
\texttt{?} means that a differential is not known to occur.

\column{drtarget:}
Value of an algebraic Novikov differential.

\newpage

\file{algNovikov-E3.csv:}
Each line of the file corresponds to an element in the
algebraic Novikov $E_3$-page.
This data is used to produce the chart appearing in \cite{IWX19a}.
This file takes the same format as
\textbf{algNovikov-E2.csv}.

\file{algNovikov-E4.csv:}
Each line of the file corresponds to an element in the
algebraic Novikov $E_4$-page.
This data is used to produce the chart appearing in \cite{IWX19a}.
This file takes the same format as
\textbf{algNovikov-E2.csv}.

\file{algNovikov-E5.csv:}
Each line of the file corresponds to an element in the
algebraic Novikov $E_5$-page.
This data is used to produce the chart appearing in \cite{IWX19a}.
This file takes the same format as
\textbf{algNovikov-E2.csv}.

\newpage

\file{algNovikov-Einfty.csv:}
Each line of the file corresponds to an element in the
algebraic Novikov $E_\infty$-page.
This data is used to produce the chart appearing in \cite{IWX19a}.

\column{name:}  Human-readable name of an element.
(Beware that naming conventions have changed over time.)

\column{stem:} The stem of an element.  This is the
horizontal coordinate in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{cell:} Indicates whether an element is detected by the top cell
or the bottom cell of the cofiber of $\tau$. An empty cell means that
an element lies beyond the range that has been analyzed. \\
\texttt{B} means that an element is in the image in homotopy 
of inclusion of the bottom cell.\\
\texttt{T} means that an element maps non-trivially in homotopy
under projection to the top cell. \\
\texttt{?} means that it is not known whether an element is detected
by the bottom cell or the top cell. \\
\texttt{!} means that there is a hidden value of inclusion of the 
bottom cell or of projection to the top cell.

\column{h0info:}
Information about special behavior of an $h_0$ extension. \\
\texttt{h} means that there is a hidden $2$ extension.

\column{h0target:}
Value of an $h_0$ extension.  An empty cell indicates
that there is no $h_0$ extension. \\
\texttt{loc} means that an element is $h_0$-periodic.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
\texttt{h} means that there is a hidden $\eta$ extension.

\column{h1target:}
Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension. \\
\texttt{loc} means that an element is $h_1$-periodic.

\column{h2info:}
Information about special behavior of an $h_2$ extension. \\
\texttt{h} means that there is a hidden $\nu$ extension.

\column{h2target:}
Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\newpage

\file{algNovikov-Einfty-extn.csv:}
Each line of the file corresponds to a hidden extension by
$2$, $\eta$, or $\nu$
in the Adams-Novikov $E_\infty$-page.  This data is used to produce the
chart appearing in \cite{IWX19a}.  Not all hidden extensions appear
in this file; only the ones that require curved lines are listed.

\column{source:}  Source of an extension.
(Beware that naming conventions have changed over time.)

\column{type:} Type of extension. \\
\texttt{h0} means an extension by $2$. \\
\texttt{h1} means an extension by $\eta$. \\
\texttt{h2} means an extension by $\nu$.

\column{stem:} The stem of the source of an extension.  This is the
horizontal coordinate in a standard Adams-Novikov chart.

\column{Adams filtration:} The Adams-Novikov filtration of 
the source of an extension.  This is the vertical coordinate in a standard 
Adams-Novikov chart.

\column{weight:} The motivic weight of an element.

\column{target:} Target of an extension.

\column{sourcex, sourcey, targetx, targety}:
Used for display purposes in reference to the chart in \cite{IWX19a},
when a curved hidden extension is necessary.
Gives the tangent vectors at the source and target.

\newpage

\section{Machine generated data}

\file{Adams-motivic-E2-machine.csv:}
Each line of the file corresponds to an $\F_2[\tau]$-module generator
of the $\C$-motivic Adams $E_2$-page.

\column{name:}
An arbitrary name of the form 
\texttt{\{a-b\}}
assigned by machine to a generator.
The value of \texttt{a} is the Adams filtration of the generator,
while the value of \texttt{b} is an arbitrary number.

\column{stem:} The stem of an element.  This is the horizontal coordinate
in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{tautorsion:} Indicates the $\tau$ module structure of a
generator. \\
\texttt{0} means that an element is $\tau$-periodic. \\
Any other integer $k$ means that a generator is annihilated by $\tau^k$.

\column{h0info:}
Information about special behavior of an $h_0$ extension. \\
An integer $k$ means that an $h_0$ extension
equals $\tau^k$ times a generator.

\column{h0target:} Value of an $h_0$ extension.  An empty cell indicates
that there is no $h_0$ extension.

\column{h1info:}
Information about special behavior of an $h_1$ extension. \\
An integer $k$ means that an $h_1$ extension
equals $\tau^k$ times a generator.

\column{h1target:} Value of an $h_1$ extension.  An empty cell indicates
that there is no $h_1$ extension.

\column{h2info:}
Information about special behavior of an $h_2$ extension. \\
An integer $k$ means that an $h_2$ extension
equals $\tau^k$ times a generator.

\column{h2target:} Value of an $h_2$ extension.  An empty cell indicates
that there is no $h_2$ extension.

\column{h3info:}
Information about special behavior of an $h_3$ extension. \\
An integer $k$ means that an $h_3$ extension
equals $\tau^k$ times a generator.

\column{h3target:} Value of an $h_3$ extension.  An empty cell indicates
that there is no $h_3$ extension.

\newpage

\file{algNovikov-machine.csv:}
Each line of the file corresponds to an element in the
algebraic Novikov $E_2$-page.

\column{name:}
An arbitrary name 
assigned by machine to a generator.

\column{stem:} The stem of an element.  This is the horizontal coordinate
in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{h0target:} Value of an $h_0$ extension
in the Adams-Novikov $E_2$-page.  An empty cell indicates
that there is no $h_0$ extension.
Beware that these are not extensions in the algebraic Novikov
$E_2$-page.

\column{h1target:} Value of an $h_1$ extension in the 
Adams-Novikov $E_2$-page.  An empty cell indicates
that there is no $h_1$ extension. 
Beware that these are not extensions in the algebraic Novikov
$E_2$-page. \\
\texttt{loc} indicates that an element is $h_1$-periodic.

\column{h2target:} Value of an $h_2$ extension in the Adams-Novikov
$E_2$-page.  An empty cell indicates
that there is no $h_2$ extension.
Beware that these are not extensions in the algebraic Novikov
$E_2$-page.

\column{h3target:} Value of an $h_3$ extension in the Adams-Novikov
$E_2$-page.  An empty cell indicates
that there is no $h_3$ extension.
Beware that these are not extensions in the algebraic Novikov
$E_2$-page.

\column{drinfo:}
Information about an algebraic Novikov differential. \\
An integer value $r$ indicates a $d_r$ differential.

\column{drvalue:}
Value of an algebraic Novikov $d_r$ differential.

\newpage

\file{ANSS-cofiber-2-machine.csv:}
Each line of the file corresponds to an element in the
Adams-Novikov $E_2$-page for the cofiber of $2$.

\column{name:}
An arbitrary name 
assigned by machine to a generator.

\column{cell:} \\
\texttt{B} indicates that an element lies in the image 
of the bottom cell.\\
\texttt{T} indicates that an element projects non-trivially to the
top cell.

\column{image:} 
Indicates the pre-image of an element under inclusion of the bottom cell,
or the value under projection to the top cell.

\column{stem:} The stem of an element.  This is the horizontal coordinate
in a standard Adams chart.

\column{Adams filtration:} The Adams filtration of 
an element.  This is the vertical coordinate in a standard 
Adams chart.

\column{weight:} The motivic weight of an element.

\column{Adams-Novikov filtration:} The Adams-Novikov filtration
of an element.  This is the vertical coordinate in a standard
Adams-Novikov chart.

\column{h1target:} Value of an extension by \texttt{[1-0]}, i.e.,
by $h_1$.
An empty cell indicates that there is no extension.

\column{h2target:} Value of an extension by \texttt{[1-1]}, i.e., 
by $h_2$.
An empty cell indicates that there is no extension.

\column{h3target:} Value of an extension by \texttt{[1-2]}, i.e.,
by $h_3$.
An empty cell indicates that there is no extension.

\column{theta2:} Value of an extension by \texttt{v2\^{}1[1-0]}, i.e.,
by the element
that maps to $h_2^2$ under projection to the top cell.

\column{theta3:} Value of an extension by \texttt{[1-3]}, i.e.,
by the element
that maps to $h_3^2$ under projection to the top cell.

\column{theta4:} Value of an extension by \texttt{[1-4]}, i.e.,
by the element
that maps to $h_4^2$ under projection to the top cell.

\column{theta5:} Value of an extension by \texttt{[1-5]}, i.e.,
by the element
that maps to $h_5^2$ under projection to the top cell.

\newpage

\file{ANSS-conversion-machine.csv:}
Converts between arbitrary names for elements in the Adams-Novikov
$E_2$-page used in the two previous machine-generated files.

\column{ANSS-cofiber-2-machine:}
Used in the \column{image} column of 
\file{ANSS-cofiber-2-machine.csv}.

\column{algNovikov-machine:}
Used in the \column{name} column of
\file{algNovikov-machine.csv}.

\newpage

\setlength{\parskip}{0pt}

\bibliographystyle{amsalpha}
\begin{bibdiv}
\begin{biblist}

\bib{IWX19b}{article}{
	author={Isaksen, Daniel C.},
	author={Wang, Guozhen},
	author={Xu, Zhouli},
	title={More stable stems},
	status={preprint},
	date={2019},
}

\bib{IWX19a}{article}{
	author={Isaksen, Daniel C.},
	author={Wang, Guozhen},
	author={Xu, Zhouli},
	title={Classical algebraic Novikov charts and $\C$-motivic Adams charts for the cofiber of $\tau$},
	date={2019},
	status={preprint},
}

\bib{IWX19c}{article}{
	author={Isaksen, Daniel C.},
	author={Wang, Guozhen},
	author={Xu, Zhouli},
	title={Classical and $\C$-motivic Adams charts},
	status={preprint},
	date={2019},
}

\bib{IWX19d}{article}{
	author={Isaksen, Daniel C.},
	author={Wang, Guozhen},
	author={Xu, Zhouli},
	title={Adams-Novikov charts},
	status={preprint},
	date={2019},
}


\end{biblist}
\end{bibdiv}


\end{document}