% part08_networks.tex — Part VIII, Scientific Knowledge Networks (Agent L/I, 2026-11-03).
% Every corpus number is a macro from tables/numbers.tex or appears in a generated table (tables/make_tables.py).
% Result files: results/bibliometrics/*.csv (corpus v2, 2026-11-03 18:0x) and results/graph/cited_age_yearly.csv (v1, pending v2).

\section{Scope and reading rules}
\label{sec:net-scope}

This part reports what the eligible corpus shows about the people, organisations, countries and venues that
produce computer-science research, about the distribution of attention over the works they produce, and about
the sources on which that research draws. It is the empirical counterpart of research questions RQ4 and RQ6
and of the networks section of the methodology (Section~\ref{sec:m-networks}), and it tests the parts of
hypotheses H4, H5 and H6 that the current result files make testable. The citation-flow statistics between
taxonomy categories, which carry the main weight of H4, depend on the classification of Part~IX and are not
yet available; Section~\ref{sec:net-flows-categories} is a placeholder for them. The reader should
therefore expect a part that is complete on collaboration, geography, institutions, venues and aggregate
citation structure, and provisional on knowledge flows.

Three reading rules apply throughout. First, every indicator is computed on the eligible corpus defined in
Part~III (Section~\ref{sec:data-eligibility}), so that ``computer science'' means the union of DBLP-indexed,
OpenAlex-primary-field and arXiv \texttt{cs} works after the exclusions of the PRISMA flow, and the indicators
inherit the boundary decisions and the affiliation completeness of that corpus. Second, the two periods of the
protocol are unequal in length and in completeness: the baseline runs from January 2018 to the end of
November 2022, the post period from December 2022 to the snapshot of October 2026 completed by the API
increment, and the last year of the post period is partial for the reasons set out in
Section~\ref{sec:data-dates}. Tables by year therefore carry 2026 as an incomplete row, and the fixed-window
citation statistics of Section~\ref{sec:net-citations} are complete only up to the publication years flagged in
Table~\ref{tab:citation_windows}. Third, the comparison of periods is descriptive. The protocol states the
hypotheses with a direction so that null and opposite results can be reported as such, and several of the
results below are of that kind; none of them is evidence of an effect of any single event, and the language of
this part is deliberately that of association and composition.

The part is organised from the smallest unit of production outward. Section~\ref{sec:net-teams} describes
authorship and team structure; Section~\ref{sec:net-international} the international co-authorship network;
Section~\ref{sec:net-geography} the geography of output; Section~\ref{sec:net-institutions} institutions and
sectors, including the industry share that H6 concerns; Section~\ref{sec:net-venues} publication channels and
venue concentration; Section~\ref{sec:net-citations} the distribution of citations and its inequality;
Section~\ref{sec:net-flows} the inflows of knowledge from other fields and the age of the works cited;
Section~\ref{sec:net-boundaries} the boundary of the database itself, through the DBLP-only records and the
\texttt{created\_date} diagnostic; and Section~\ref{sec:net-hypotheses} collects the verdicts on H4--H6.

\section{Authorship and team structure}
\label{sec:net-teams}

The long-run growth of team size in science is one of the most replicated findings of scientometrics:
\citet{wuchty2007teams} documented the shift from solo to team production across fields over five decades,
\citet{lariviere2015teamsize} extended the series back to 1900 and showed that the citation advantage of teams
has grown with it, and \citet{milojevic2014teams} proposed a generative account in which a core of small,
``Poisson-like'' teams coexists with an expanding tail of large ones. Computer science has long been a field of
small teams by the standards of the laboratory sciences, which is why the question for this corpus is not
whether teams grow but whether the rate of growth or the shape of the distribution changes across the 2022
boundary. The hypothesis set of the protocol does not take a position on team size, and the evidence is
reported for its own sake and as a control for the collaboration indicators that follow.

Table~\ref{tab:collaboration} gives the annual series, and Figure~\ref{fig:collaboration} plots the mean and the
tail shares. The mean number of authors per eligible work rises from
\VolumeYearlyTwoZeroOneEightMeanAuthors{} in 2018 to \VolumeYearlyTwoZeroTwoTwoMeanAuthors{} in 2022 and
\VolumeYearlyTwoZeroTwoFiveMeanAuthors{} in 2025, a monotone increase at a pace that does not visibly change at
the boundary; the median stays at three authors in every year, so the growth of the mean is a growth of the
upper tail. The tail shares in the table make the same point: the share of works with five or more authors
rises steadily, and the share with ten or more, although small, roughly triples over the window. The
single-author share falls through 2022 and then rises again, sharply in 2025 and 2026. That reversal is not a change in
research practice. The column of works without any resolved country shows the same U-shape, and the
single-author and unaffiliated shares move together because the records that enter the corpus fastest after
publication (preprints, repository deposits, records not yet enriched with affiliations) are also those whose
authorship metadata is least complete; as those records are enriched and matched to their published versions
in later snapshots, both shares fall. The 2025 and 2026 rows of Table~\ref{tab:collaboration} must therefore
be read as a snapshot of the indexing process as much as of authorship, and the pre-2024 trend is the only
part of the series on which a substantive statement rests.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_collaboration.pdf}
\caption{Team size, international co-authorship and industry participation by year. Mean authors per work and
tail shares from \texttt{team\_size\_yearly.csv}; the international share is the ICS of Part~IV (works with
two or more countries among works with at least one); the company share is over works with at least one
typed affiliation (\texttt{industry\_share\_yearly.csv}). 2026 is incomplete.}
\label{fig:collaboration}
\end{figure}

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_collaboration}\endgroup

The multi-institution share, the fraction of works whose authors list more than one distinct institution,
follows the mean team size through 2022 and then declines, with the same affiliation-completeness
explanation as the single-author reversal: an unaffiliated record cannot be multi-institutional. Here the
substantive literature gives a reason to expect genuine growth. \citet{jones2008multiuniversity} showed that
multi-university collaboration had become the fastest-growing form of team production in the United States,
with a citation premium concentrated in the top-tier institutions, and \citet{adams2013fourthage} argued
that a ``fourth age'' of research organised around international networks of elite institutions was
displacing the national systems of the previous one. The corpus is consistent with continued growth of
multi-institution work up to the point where the affiliation data become unreliable and is silent beyond it.

Two cautions apply to all of these shares, and they are not specific to this corpus. The first is that
OpenAlex author counts are taken from the authorship lists of the surviving record after deduplication
(Section~\ref{sec:m-dedup}); where a preprint and its published version differ in author list, the published
version wins, which is the appropriate choice but one that makes the count depend on the linkage. The second
is that very large author lists in computer science come disproportionately from a few genres, namely
consortium reports, shared-task overviews and large model ``technical reports'', so that the ten-plus share
measures the prevalence of those genres as much as the size of ordinary research teams. The disruption
literature attaches a substantive interpretation to team size, with \citet{wu2019disruption} reporting that
small teams produce more disruptive work and large teams more developmental work; that interpretation is
not tested here, because the disruption index requires a citation graph with a long post-publication horizon
that the post period does not yet provide.

\section{International co-authorship}
\label{sec:net-international}

International collaboration has grown in every field and every country for which long series exist
\citep{wagner2015cooperation, wagner2017collaboration}, and the growth has been described as the emergence
of a self-organising global network with a core group of countries that is stable over time
\citep{leydesdorff2008core}. The protocol's H6 predicts, against this background, that the international
co-authorship share of computer science does \emph{not} rise in the post period. The prediction was motivated
by two considerations stated in the protocol discussion: the geopolitical restriction of some
bilateral channels after 2020, and the shift of a growing share of the field's output into
preprint channels and into countries whose output is predominantly domestic.

The international collaboration share (ICS, Section~\ref{sec:m-bibliometrics}) is computed among works with
at least one resolved country, so that the affiliation-completeness problem of the previous section does not
enter the denominator. Its yearly values are in the last column of Table~\ref{tab:collaboration} and are
macro-reported here for the end points: \InternationalCollabYearlyTwoZeroOneEightShareIntl{} in 2018,
\InternationalCollabYearlyTwoZeroTwoZeroShareIntl{} in 2020, \InternationalCollabYearlyTwoZeroTwoTwoShareIntl{}
in 2022, \InternationalCollabYearlyTwoZeroTwoFourShareIntl{} in 2024 and
\InternationalCollabYearlyTwoZeroTwoFiveShareIntl{} in 2025. The series is flat to slightly declining: it
peaks in 2020, is lower in every subsequent year, and the post-period values are below every baseline value.
The null part of H6 is therefore supported in the direction stated, and the result is in fact stronger than
the hypothesis, which only predicted the absence of a rise. Two qualifications prevent a stronger reading.
The denominator grows faster than the numerator over the window
(\InternationalCollabYearlyTwoZeroOneEightN{} works with a country in 2018 against
\InternationalCollabYearlyTwoZeroTwoFiveN{} in 2025), and the composition of that growth, examined in the next
section, is dominated by countries with low international shares; a constant propensity to collaborate within
every country would produce exactly this aggregate decline. And the share is a share of works, not of
authors or of citations, so that the increasing size of international teams noted by
\citet{wagner2017collaboration} would not register in it.

The structure of the network behind the share is summarised in Tables~\ref{tab:country_network} and~\ref{tab:country_pairs}, which are built from the edge list of country pairs with at least fifty joint works
in a period. The threshold is a reporting choice (Section~\ref{sec:m-bibliometrics}); it keeps the network to
the pairs whose weight is robust to small linkage errors, at the cost of excluding the long tail of weak ties
through which, in the account of \citet{leydesdorff2008core}, peripheral countries enter the core. On this
restricted network, the number of edges and the number of countries both increase from the baseline to the
post period even though the post period is about ten months shorter, so the network densifies at the
threshold. The ordering of countries by strength, the sum of a country's edge weights, changes at the top:
the United States has the largest strength in the baseline and China in the post period, with the United
Kingdom third in both. The twenty strongest pairs (Table~\ref{tab:country_pairs}) show where the change comes
from. The China--United States pair is the heaviest edge in both periods, but its weight is lower in the post
period than in the baseline in absolute terms, while the pairs of China with Hong Kong, Singapore, the United
Kingdom and Australia rise in weight, and Hong Kong and Singapore rise in rank; the China--Hong Kong pair
moves from fourth to second.
The share of the China--United States edge in the total weight of the network falls accordingly
(Table~\ref{tab:country_network}). A decline in the absolute volume of joint work between the two largest
producers, in a period in which the output of both grew, is the most distinctive structural feature of the
collaboration data, and it is consistent with the bilateral-restriction channel that motivated H6; it is
not, on its own, evidence about the cause, and the reader should note that Hong Kong and Macau carry their
own country codes in OpenAlex, so that part of the apparent reorientation of China's collaboration is a
reorientation toward its own special administrative regions.

Most of the rest of the pair table is continuity. The United Kingdom--United States, Germany--United
States and Germany--United Kingdom pairs keep approximately their weights; the India--United States pair
rises; the Canada--China and Canada--United States pairs fall slightly; and the France--United States and
Australia--United States pairs fall more and drop in rank, two movements that the table records and this
part does not explain. The picture is that of a core group whose composition is stable, as
\citet{leydesdorff2008core} and \citet{glanzel2001national} found for science as a whole, with one edge
weakening and a cluster of East-Asian edges strengthening. Degree-based statistics of the network
(density, clustering, assortativity) are not reported, because at a fixed weight threshold they measure
the growth of the corpus as much as the structure of collaboration; the strength ordering and the pair
weights, which are counts, are the statistics that survive that objection.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_country_network}\endgroup
\input{tables/tab_country_pairs}

\section{The geography of production}
\label{sec:net-geography}

The country-level composition of output is the part of this study where the counting convention matters
most, and the methodology (Section~\ref{sec:m-bibliometrics}) reports both. Under full counting a work with
authors in three countries is counted once for each; under fractional counting it is divided among them.
The two conventions give different levels, and the difference is itself informative, because a country whose
full-count share is much larger than its fractional share is one whose output is predominantly
collaborative \citep{gauffriau2008counting, waltman2015counting}. Table~\ref{tab:countries} gives the
fractional counts of the fifteen largest countries by year, Table~\ref{tab:country_shares} the corresponding
shares, Table~\ref{tab:country_concentration} the concentration of the distribution and the full-count shares
of the two largest producers, and Figure~\ref{fig:country_shares} the shares of the eight largest.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_country_shares.pdf}
\caption{Country shares of eligible output under fractional counting, eight largest countries by cumulative
output. Each work is divided equally among its distinct author countries; works without a resolved country
are excluded. Source: \texttt{results/bibliometrics/countries\_yearly.csv}. 2026 is incomplete.}
\label{fig:country_shares}
\end{figure}

The dominant movement is the rise of China's share, which is already the largest in 2018 and grows in every
complete year of the window, under both counting conventions. The second is the decline of the United
States' share, which is monotone through 2025 under both conventions and recovers only in the incomplete
2026 row, where the fast channels in which American output is over-represented (preprint servers) weigh more
than they will once the year is fully indexed. The third is the growth of India and, more sharply in
relative terms, Indonesia, which enters the top five by the end of the window; the fourth is the slow
relative decline of the large European producers, Japan and Korea, whose absolute output is flat or rising
(Table~\ref{tab:countries}) while the total grows. The Russian series falls after 2021 and does not
recover. These movements are gradual and are visible in the baseline as well as in the post period;
nothing in the country shares changes direction at the 2022 boundary, and the growth of China's share is
if anything slower in 2024 and 2025 than in 2021 and 2022.

The China part of H6 asks whether the share of works with China-affiliated authors rises in the post period
\emph{in the AI categories}. The aggregate rise is established by Table~\ref{tab:country_concentration},
whose column of works with a China-affiliated author is the quantity the hypothesis names; the category-specific version requires the
classification and is \pending{China share by category after classification}. The aggregate result is,
however, weaker evidence than it looks, because the rise is a continuation of a trend that predates the
window and is documented in every recent comparison of national output
\citep{bornmann2021growth}; a test of H6 that would be informative must compare the post-period
growth of China's share in AI categories with its growth in the rest of computer science, which is what the
pending analysis will do.

Concentration across countries, measured by the Herfindahl--Hirschman index of fractional shares and by the
shares of the five and ten largest countries, rises through 2025 (Table~\ref{tab:country_concentration}).
The index is dominated by the largest share, so the rise is mostly China's rise; the top-ten share moves
less than the top-five share, which means that the countries ranked six to ten lose share to those ranked
one to five rather than to the tail. The number of countries with any output is stable. The widely
discussed concern that the geography of AI research is narrowing \citep{klinger2020narrowing,
ahmed2020dedemocratization} is a concern about institutions and compute rather than about countries, and the
country-level concentration measured here speaks to it only indirectly; the institutional evidence is in the
next section.

The ratio of a country's full count to its fractional count, in the last two columns of
Table~\ref{tab:country_concentration}, exceeds one by the extent to which its works are co-authored with
other countries, and it is informative about collaboration intensity. China's ratio is lower than the United
States' in every year, which is the signature of a more domestic output: a larger fraction of
Chinese-affiliated works has only Chinese affiliations. Since China's share grows and the
United States' falls, the aggregate international share of Section~\ref{sec:net-international} is pulled
down by composition even if no country's propensity to collaborate changes. This is the mechanical
channel behind the null result on international collaboration, and it is the reason that result is
reported with the composition caveat rather than as a change in behaviour.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_countries}\endgroup
\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_country_shares}\endgroup
\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_country_concentration}\endgroup

\section{Institutions and sectors}
\label{sec:net-institutions}

\subsection{The sectoral mix of affiliations}

OpenAlex types every institution as education, facility, company, government, healthcare, nonprofit,
funder, archive or other. Table~\ref{tab:institution_types} gives the distribution of typed affiliations over
these classes by year, and Table~\ref{tab:industry} the share of works with at least one company affiliation,
which is the statistic named by H6. The hypothesis predicts that the industry share rises in the post period
in AI categories. The prediction follows a line of work that has documented the growing weight of industry in
machine-learning research: \citet{frank2019citationgraphs} traced the shift of the AI citation graph toward
industry-authored and computer-science-internal sources, \citet{ahmed2023industry} reported that industry's
share of the largest models, of the most cited papers and of the field's PhD graduates had risen sharply in
the decade to 2022, and \citet{klinger2020narrowing} argued, in a preprint, that the thematic diversity of AI
research had narrowed as the private sector's share rose.

The aggregate corpus does not show a rising industry share. The company share of works with a typed
affiliation is \IndustryShareYearlyTwoZeroOneEightShareCompany{} in 2018, rises to a maximum of
\IndustryShareYearlyTwoZeroTwoOneShareCompany{} in 2021, and then falls in every subsequent year to
\IndustryShareYearlyTwoZeroTwoFiveShareCompany{} in 2025, which is below the 2018 value; the incomplete
2026 row is at \IndustryShareYearlyTwoZeroTwoSixShareCompany{}. The absolute number of works with a company
affiliation keeps growing (\IndustryShareYearlyTwoZeroOneEightNCompany{} in 2018 against
\IndustryShareYearlyTwoZeroTwoFiveNCompany{} in 2025), so the falling share is a matter of the denominator
growing faster: the growth of the post-period corpus comes disproportionately from education-sector output,
and within that from the countries of Section~\ref{sec:net-geography} whose output is almost entirely
academic. Table~\ref{tab:institution_types} shows the same thing from the other side, with the education
share of affiliations rising through the window and the facility, government and company shares all giving
way. The aggregate part of H6 is therefore not supported; the sign is opposite to the one predicted. Whether
the category-specific version holds, that is, whether the company share rises within the AI categories while
falling in the aggregate, is exactly the kind of composition question that the aggregate cannot settle, and it
is \pending{industry share by category after classification}.

The result is less at odds with the cited literature than it seems, for three reasons that matter for its
interpretation. \citet{ahmed2023industry} measure industry's presence at the frontier---the largest models,
the most cited papers, the leading conferences---and not its share of all output; a sector can dominate the
frontier of a field while its share of the field's total publications falls, and the two facts are compatible
with a frontier that is increasingly expensive to reach \citep{ahmed2020dedemocratization}. Second, the
OpenAlex institution type is assigned to the institution, not to the author's role, so a work by a
corporate research laboratory published with an academic co-author counts as both, and the share reported
here is the share of works with \emph{any} company affiliation, which is the most inclusive definition.
Third, the affiliation completeness problem of Section~\ref{sec:net-teams} affects the typed denominator:
records without affiliation data are excluded, and if industry-authored preprints are less often enriched
with affiliations than journal articles, the company share of recent years is understated. None of these
reasons reverses the aggregate finding, but together they confine it to what it measures.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_industry}\endgroup
\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_institution_types}\endgroup

\subsection{Institutional concentration and stability}

The institution tables (Tables~\ref{tab:institution_concentration} and~\ref{tab:top_institutions}) list
institutions with at least two hundred works in a period, identified by their OpenAlex identifiers only; the
result files do not carry institution names, and this part refrains from resolving the identifiers by hand so
that every statement remains reproducible from the released artefacts. The number of institutions above the
threshold rises from the baseline to the post period, as does the number of works they account for, in both
counting conventions. The ratio of full to fractional counts among the largest institutions is close to two,
meaning that the average work of a large institution carries about one other institution, which is the
multi-institution pattern of Section~\ref{sec:net-teams} seen from the institution's side.

Concentration among the listed institutions is low and stable: the ten largest account for a few per cent of
the listed fractional output and the hundred largest for less than a quarter, with both shares slightly
higher in the post period. This is a different picture from the one that the concern over the
``de-democratisation'' of AI research conveys \citep{ahmed2020dedemocratization}, and the difference is again
one of object: the distribution of \emph{all} computer-science output over institutions is wide, whereas the
distribution of the frontier of one sub-area may be narrow, and only the latter has been claimed to be
narrowing. The rank stability of institutions across periods is high: of the institutions listed in the
baseline, the great majority are also listed in the post period, and the Spearman correlation of their
fractional counts across the two periods, given in the note to Table~\ref{tab:institution_concentration}, is
close to nine tenths. Among the institutions listed in both periods, the twenty-five largest of the post period
(Table~\ref{tab:top_institutions}) have post-to-baseline ratios that cluster around or somewhat above the
ratio of the two periods' listed totals, with a few institutions growing considerably faster and two of the
largest full-count producers growing slower than the corpus. The institutional hierarchy of computer science, in other words, was not reshuffled in the
post period; it grew in place.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_institution_concentration}\endgroup
\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_top_institutions}\endgroup

\section{Publication channels and venue concentration}
\label{sec:net-venues}

The venue is the unit at which the publishing system intersects the research system, and the two have been
changing in opposite directions in computer science for two decades: the publishing side has consolidated
into a small number of commercial and society publishers \citep{lariviere2015oligopoly}, while the research
side has moved a growing share of its first dissemination to arXiv
\citep{sutton2017arxivcs, lin2020arxivcs, lariviere2014arxiv}. The OpenAlex notion of source, on which the
tables of this section are built, follows the venue (a journal, a conference series, a book series, a
repository, an ebook platform) rather than the publisher, so what is measured here is concentration over
venues, and arXiv counts as one venue. The protocol's H5 anticipated this when it predicted that venue
concentration would be ``stable or lower because of preprint growth'' once the preprint source is treated
separately; the methodology (Section~\ref{sec:m-bibliometrics}) notes that the index with arXiv included
rises mechanically with preprint growth.

Table~\ref{tab:venue_hhi} and Figure~\ref{fig:venue_concentration} give the yearly number of distinct sources,
the Herfindahl--Hirschman index over sources and the share of the largest source. The number of distinct
sources rises every complete year, from \VenueHhiYearlyTwoZeroOneEightNSources{} in 2018 to
\VenueHhiYearlyTwoZeroTwoFiveNSources{} in 2025, so the venue landscape is widening in the sense of variety.
The index, however, rises as well: from \VenueHhiYearlyTwoZeroOneEightHhi{} in 2018 to
\VenueHhiYearlyTwoZeroTwoFiveHhi{} in 2025 and \VenueHhiYearlyTwoZeroTwoSixHhi{} in the incomplete 2026
row, and the share of the largest source, which is arXiv in every year, goes from
\VenueHhiYearlyTwoZeroOneEightTopOneShare{} to \VenueHhiYearlyTwoZeroTwoFiveTopOneShare{} and then to
\VenueHhiYearlyTwoZeroTwoSixTopOneShare{} in 2026. The index is small in absolute terms (its upper bound is
one, reached when a single venue carries all works), and the squared share of arXiv accounts for most of it
in the later years; the 2026 value is an artefact of right truncation, since preprints are indexed within
days and journal and conference records months later (Section~\ref{sec:data-dates}), and will fall as the
year completes. The concentration result is therefore the one the protocol expected in mechanism and the
opposite of the one it expected in sign: concentration over venues, with arXiv counted as a venue, rises
because of preprint growth, and the version of the index without the preprint type, which H5 names, is
\pending{venue HHI excluding preprints}. The qualitative conclusion that does not depend on it is that the
rest of the venue landscape is not concentrating: the number of venues grows, and the second-ranked sources
in Table~\ref{tab:top_sources} hold shares that are an order of magnitude below arXiv's.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_venue_concentration.pdf}
\caption{Number of distinct sources per year (left) and venue concentration (right): Herfindahl--Hirschman
index over sources, scaled by $10^4$, and share of the largest source, which is arXiv in every year.
Source: \texttt{results/bibliometrics/venue\_hhi\_yearly.csv}. 2026 is incomplete and inflated by the
faster indexing of preprints.}
\label{fig:venue_concentration}
\end{figure}

Tables~\ref{tab:source_types} and~\ref{tab:top_sources} describe the channels themselves. By source type,
journals carry about half of the listed works in both periods, conferences between a fifth and a quarter,
and repositories rise from about an eighth to about a fifth between the baseline and the post period, at
the expense of conferences, book series and ebook platforms. The twenty largest sources make the composition concrete. arXiv
is first in both periods and more than doubles its count; Lecture Notes in Computer Science is second in both;
SSRN, which is not a computer-science venue but hosts a growing number of works that OpenAlex classifies in the
field, moves from the lower part of the baseline list to third; Research Square and NeurIPS enter the
post-period list and the AAAI conference proceedings rise within it; the large open-access
journals (IEEE Access, Sensors, Remote Sensing) remain in the list but with lower counts in the post period
than in the baseline, a decline whose cause (editorial policy, reclassification by OpenAlex, or the shorter
period) the corpus does not identify. The
appearance of generalist repositories (SSRN, Research Square, OSF) among the largest computer-science
sources is a boundary effect of the OpenAlex topic classification rather than a change in where computer
scientists publish, and it is one of the reasons the strict-core sensitivity set of Part~III exists.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_venue_hhi}\endgroup
\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_source_types}\endgroup
\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_top_sources}\endgroup

\section{The distribution of citations}
\label{sec:net-citations}

\subsection{Levels, zeros and inequality within fixed windows}

Citation distributions are heavy-tailed in every field, and the degree of skewness is remarkably similar
across fields once counts are normalised by the field mean \citep{seglen1992skewness, radicchi2008universality,
albarran2011skewness}. The mechanisms proposed for the tail are cumulative advantage, the ``Matthew effect''
by which recognised work attracts recognition \citep{merton1968matthew, price1976cumulative}, and its
network formalisation as preferential attachment \citep{barabasi1999scaling}; the mechanism proposed for the
mass of the distribution is a combination of a work's intrinsic fitness and an ageing function
\citep{wang2013longterm}. What a cross-period comparison can measure is not these mechanisms but the shape
of the distribution at a fixed exposure, and the fixed windows of Section~\ref{sec:m-citations} are the device
that makes the shape comparable: $c^{(36)}$ counts the citations received in the publication year and the two
following calendar years, and is complete for publication years up to 2023.

Table~\ref{tab:citation_windows} and Figure~\ref{fig:citation_inequality} give the yearly statistics. The mean
of $c^{(36)}$ rises from \CitationWindowsYearlyTwoZeroOneEightMeanCThreeSix{} for works published in 2018 to
\CitationWindowsYearlyTwoZeroTwoTwoMeanCThreeSix{} for 2022 and
\CitationWindowsYearlyTwoZeroTwoThreeMeanCThreeSix{} for 2023, the last complete year; the median is one
citation in most years and two in 2022, so the mean is carried by the tail. The share of works uncited at
three years falls from \CitationWindowsYearlyTwoZeroOneEightShareUncitedThreeSix{} for 2018 to
\CitationWindowsYearlyTwoZeroTwoTwoShareUncitedThreeSix{} for 2022 and rises again to
\CitationWindowsYearlyTwoZeroTwoThreeShareUncitedThreeSix{} for 2023. Both movements are what a growing
citing population produces: each publication year is cited by the following two years' output, and that output
grows, so later cohorts receive more citations at equal exposure \citep{bornmann2015growth}. The reversal in
2023 is the first sign of right truncation in the window, since the third calendar year of the 2023 cohort
is 2025, for which the increment of Part~III is complete but the slower channels of indexing are not; it is
flagged in the table and is the reason the 2024 row, whose window is formally incomplete, is not used.

The Gini coefficient of $c^{(36)}$ is the inequality statistic named, with a deviation in window length
recorded in Section~\ref{sec:m-bibliometrics}, by H5. It falls from
\CitationWindowsYearlyTwoZeroOneEightGiniCThreeSix{} for 2018 to
\CitationWindowsYearlyTwoZeroTwoTwoGiniCThreeSix{} for 2022, then rises to
\CitationWindowsYearlyTwoZeroTwoThreeGiniCThreeSix{} for 2023; the 12-month Gini follows the same path at a
slightly higher level, as expected from the larger share of zeros in the shorter window. Since the share of
uncited works moves with the Gini, and uncited works are the main contributor to inequality in a short window
(Section~\ref{sec:m-bibliometrics}), the fall through 2022 is to a large extent a fall in the share of zeros
rather than a change in the shape of the tail, and the 2023 uptick is the truncation effect just described.
H5 predicts that citation inequality is higher in the post period than in the baseline \emph{for AI
categories}. The aggregate series can test only the aggregate statement, and for the one post-period
publication year with a complete window (2023) the aggregate Gini is above the 2022 value and below every
baseline value before 2021, so the aggregate evidence is mixed and dominated by truncation; the category
version of the test, which is the one the hypothesis states, is \pending{Gini by category after classification}.
The reader should also weigh the finding of \citet{nielsen2021inequality} that global citation inequality has
risen over several decades when measured on long windows across all fields; the three-year windows used here
measure a different quantity, early attention, whose inequality is driven by zeros, and the two results are
not in contradiction.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_citation_inequality.pdf}
\caption{Fixed-window citation levels and inequality by publication year, for years with a complete
36-month window. Left: mean $c^{(36)}$ and the 99th percentile divided by ten. Right: Gini coefficient of
$c^{(36)}$ and share of works uncited at 36 months. Source:
\texttt{results/bibliometrics/citation\_windows\_yearly.csv}.}
\label{fig:citation_inequality}
\end{figure}

The field-weighted citation impact supplied by OpenAlex, reported for comparison in
Table~\ref{tab:citation_windows}, has a mean above one in every year, which says that the eligible corpus is
cited above the OpenAlex world average for works of the same type, year and subfield; its median is below
one in every year, which says that the typical computer-science work is not. The two statements together
are the skewness result once more. The mean FWCI declines slowly, though not monotonically, across cohorts and the median rises through
2022 and collapses for 2025 and 2026, where the exposure is too short for the indicator to mean anything;
the methodology's reservations about FWCI (Section~\ref{sec:m-bibliometrics}) are borne out and the
indicator is not used further.

\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_citation_windows}\endgroup

\subsection{The most cited works and what they reveal about the database}

Table~\ref{tab:top_cited} lists the ten works with the largest $c^{(36)}$ in each publication year from 2018
to 2025, with their total citations to date. The list is reported because research question RQ3 asks for the
most influential contributions and because the mandate requires that the manuscript identify them; it is
reported with its errors visible because the errors are instructive. Three kinds of entry appear. The first
is the expected one: the foundational works of the deep-learning decade are present with the citation counts
one would expect, among them \emph{Deep Contextualized Word Representations}, \emph{MobileNetV2} and
\emph{Squeeze-and-Excitation Networks} for 2018, \emph{BERT} for 2019, \emph{Momentum Contrast} and
\emph{A Simple Framework for Contrastive Learning} for 2020, the \emph{Vision Transformer} and the
\emph{Swin Transformer} for 2021, \emph{High-Resolution Image Synthesis with Latent Diffusion Models} and
\emph{Masked Autoencoders Are Scalable Vision Learners} for 2022, \emph{Segment Anything} and
\emph{YOLOv7} for 2023, and \emph{DeepSeek-R1} for 2025, together with the scientific-software and
bioinformatics-resource papers (SciPy, NumPy, STRING, SWISS-MODEL, iTOL, AlphaFold Protein Structure
Database, UniProt, KEGG) that the OpenAlex topic classification places in computer science and that are
among the most cited works of any field.

The second kind of entry is a duplicate or misdated record of a canonical work: \emph{Bitcoin: A Peer-to-Peer
Electronic Cash System} appears as an SSRN record dated 2019 and again dated 2022, \emph{Generative
Adversarial Nets} as a 2023 book chapter, \emph{Batch Normalization} as a 2024 preprint, \emph{Learning
Multiple Layers of Features from Tiny Images} as a 2024 article, and \emph{Attention Is All You Need} as a 2025
preprint. These are not errors of this study's deduplication, which merges a preprint with its published
version within the window (Section~\ref{sec:m-dedup}); they are distinct OpenAlex works, with their own
identifiers and their own citation counts, created when a reference string resolved to a new record rather
than to the existing one, and dated by the record rather than by the work. Their $c^{(36)}$ is large because
the citations of a canonical work accrue to whichever record the citing works' reference strings resolve to.
The third kind is the inconsistent record: entries whose window count exceeds their total count, or whose
total count is zero while their window count is in the thousands, including several records of the Dagstuhl
DROPS series and of regional journals whose titles bear no relation to the citation volume attached to
them. These are, to the best of the author's understanding, artefacts of OpenAlex's reference matching,
where a frequently cited string has been mapped to a wrong target; they are recognisable precisely because
the two counts disagree, and \citet{alperin2024openalex} and \citet{culbert2025openalexcoverage} document
related inconsistencies in OpenAlex citation data at the aggregate level.

The consequences for this part are limited but must be stated. The aggregate citation statistics of the
previous subsection are insensitive to a small number of misattributed records among hundreds of
thousands per year, except through the maximum and the 99th percentile, which Table~\ref{tab:citation_windows} reports and
which should not be interpreted. The identification of the most influential works for RQ3, by contrast,
cannot rely on a ranked list from the database without a record-level audit, and the audit must check the
consistency of window and total counts, the uniqueness of the work across records, and the agreement of the
record's date with the work's first appearance. That audit is part of the human-review checkpoint on RQ3 and
is \pending{record-level audit of the top-cited lists}; until it is done, the titles above are quoted as what
the database returns, not as a ranking endorsed by this study. The lesson for the field-normalised scores
of Section~\ref{sec:m-citations} is the same as the one \citet{waltman2016review} draw for all mean-based
indicators: a reference class containing one record with tens of thousands of misattributed citations has a
mean that is wrong for every work in the class, and the normalised scores of Part~IX should be computed
after the exclusion of records failing the consistency check; whether the current pipeline applies that
exclusion is \pending{NCS computed after exclusion of inconsistent records}.

\begingroup\footnotesize\setlength{\tabcolsep}{4pt}\input{tables/tab_top_cited}\endgroup

\section{Knowledge inflows and the age of cited work}
\label{sec:net-flows}

\subsection{Where the references of computer science point}
\label{sec:net-flows-fields}

Research question RQ4 asks how citation networks and interdisciplinary knowledge flows have evolved, and
H4 predicts that the share of citations crossing area boundaries rises in the post period. The methodology
defines two levels at which flows are measured: between the taxonomy categories of this study, through the
flow matrices of equation~\eqref{eq:flow}, and between the corpus and the rest of the literature, through the
external edge set of Section~\ref{sec:m-citgraph}, whose cited works are typed by their OpenAlex field. Only
the second level is available at the time of writing, and only from the first version of the corpus: the
graph tables of \texttt{results/graph/} are being regenerated for corpus v2, and the field-flow file was not
present when this part was written. Figure~\ref{fig:field_inflows}, generated from the v1 file, is
described here qualitatively, and every quantitative statement about it is \pending{v2 graph}.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_field_inflows.pdf}
\caption{Share of the resolved references of eligible works, by citing year, that point to works inside the
corpus and to works outside it by cited OpenAlex field (seven largest external fields). Generated from the
corpus v1 file \texttt{results/graph/field\_flows\_yearly.csv}; to be regenerated for v2.}
\label{fig:field_inflows}
\end{figure}

The figure separates the references of each citing year into those that point inside the corpus, that is, to
computer-science works published from 2018 onward, and those that point outside it, by the cited work's
field. Its dominant feature is mechanical and must be read first: the share of references pointing inside the
corpus rises steeply with the citing year, and the share pointing to computer science outside the corpus
falls by the same amount, because the corpus starts in 2018 and a work published in 2018 cannot cite inside
it except at age zero, whereas a work published in 2026 has eight years of corpus to cite. The two
computer-science curves together are approximately flat, and their sum is the share of references that
stay within the field. The curves of the other fields are what the flow question is about, and they are
nearly flat over the window: engineering is the largest external field and declines slowly, the social
sciences, mathematics, medicine, psychology and decision sciences each hold a few per cent of references
with no visible change of direction in the post period, and medicine is the only external field whose share
rises slightly at the end of the window. On the v1 evidence the field-level version of H4 is not supported:
the boundary-crossing share of computer-science references toward other OpenAlex fields does not rise
after 2022, and the slow decline of the engineering share continues a trend visible in the baseline.

This is a weaker statement than the one H4 makes, and the difference should be kept in view. The
hypothesis concerns boundaries \emph{within} computer science (systems toward AI, security toward AI,
human--computer interaction toward AI), and a field whose sub-areas converge on a common set of methods
may well cite less outside the field, not more, as its internal frontier absorbs the attention that used to
go to mathematics or engineering. The flat external shares are therefore compatible with H4 and with its
negation, and only the category flow matrices can decide between them. What the field-level curves do
establish is a boundary condition for the interdisciplinarity literature: the diversity indices of
Section~\ref{sec:m-diversity}, whether Rao--Stirling or Leinster--Cobbold, will be computed over a reference
distribution whose external component is small and stable, so that any change they detect will come from
the internal component. \citet{porter2009interdisciplinarity} found, for six fields over three decades, that
interdisciplinarity measured on references rose slowly and mostly through neighbouring fields; the
computer-science curves are consistent with that pattern and do not show the acceleration that the
foundation-model narrative would predict.

\subsection{The age of cited work}
\label{sec:net-age}

The age of the works a field cites is the simplest measure of how fast its knowledge turns over, and the
literature disagrees on its direction. \citet{evans2008narrowing} reported that online availability narrowed
citation toward fewer and more recent works; \citet{verstak2014giants}, in a preprint based on Google Scholar,
reported the opposite, a growing share of citations to older articles; \citet{parolo2015attention} measured
an accelerating decay of attention to individual papers as the volume of publication grew; and
\citet{chu2021slowed} argued that in very large fields the growth of publication itself ossifies the canon,
because new work cannot be read widely enough to displace it. Computer science is the field in which the
turnover is expected to be fastest, and \citet{frank2019citationgraphs} found that the AI citation graph had
become more self-referential and more recent-leaning over the 2010s.

Figure~\ref{fig:cited_age} and Table~\ref{tab:cited_age} give the distribution of the age of cited works, the
citing year minus the cited work's publication year, for the resolved references of eligible works. The
cited-age file is the one graph table available at the time of writing, and it is a v1 file; the table will
be regenerated from the v2 file by the same script and its values are \pending{v2 graph}. On the v1
distribution, the mode of citation age is two years in every citing year, the mean falls monotonically from
2018 to 2025, the median falls from six to five years, the share of references to works at most five years
old rises by more than ten points over the window, and the share to works more than ten years old falls by
about the same amount. The shift is steady and does not accelerate at the 2022 boundary; the post-period
curves in the figure continue the movement of the baseline curves. A small share of references point to
works dated after the citing work, which arises from preprints cited before their published version carries
a later date and from year-only dates; this share falls over the window as the corpus's own dates become
first-appearance dates, and is excluded from the age statistics.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_cited_age.pdf}
\caption{Distribution of the age of cited works (citing year minus cited year, 0 to 30 years) for five
citing years. Generated from the corpus v1 file \texttt{results/graph/cited\_age\_yearly.csv}; to be
regenerated for v2.}
\label{fig:cited_age}
\end{figure}

The evidence therefore sides with \citet{evans2008narrowing} and \citet{parolo2015attention} rather than
with \citet{verstak2014giants} for this field and this window, with one reservation that the reference
coverage of OpenAlex imposes. If the probability that a reference string resolves to an OpenAlex record is
higher for recent, DOI-bearing works than for older ones, as \citet{culbert2025openalexcoverage} report in
their comparison with Web of Science and Scopus, then the resolved references are biased toward youth, and a
constant true age distribution would appear to become younger as the resolvable share rises. The reference
coverage table of the methodology (declared, internal and external references by year) is the control for
this and is part of the pending v2 graph; the age shift is reported here as observed, not as corrected.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_cited_age}\endgroup

\subsection{Knowledge flows between categories}
\label{sec:net-flows-categories}

The flow matrices $F_t$ between the categories of the ontology, the cross-area shares $X_{\alpha,t}$ of
equation~\eqref{eq:cross-area} and the yearly modularities $Q_{\mathrm{cat}}$ and $Q_{\mathrm{area}}$ of
equation~\eqref{eq:modularity} are the statistics on which H4 turns and the ones that would show whether
systems, security and human--computer interaction cite the AI categories more after 2022 than before. They
require the primary category of every work and are produced by
\texttt{knowledge\_graph/02\_category\_flows.py} once the classification of Part~IX is complete. The result
files \texttt{category\_flows\_yearly.csv}, \texttt{cross\_area\_share\_yearly.csv} and
\texttt{modularity\_yearly.csv} do not exist at the time of writing, and this subsection is
\pending{category flows after classification}. When it is filled, it should report, for each citing area, the
cross-area share by year with the composition-adjusted variant of Section~\ref{sec:m-networks}, the two
modularities with the self-share, and a comparison of the baseline and post means with the caveat that the
post-period citing years have shorter reference lists in the incomplete 2026 row.

\section{The boundary of the database}
\label{sec:net-boundaries}

\subsection{What DBLP sees that the corpus does not}

The corpus is the union of several sources resolved to OpenAlex records (Section~\ref{sec:data-linkage}),
and a DBLP record without an OpenAlex counterpart cannot enter it, because the citation, affiliation and
topic data on which every indicator of this part depends are OpenAlex's. Table~\ref{tab:dblp_only} counts
these records by DBLP type and year. They are a small fraction of DBLP's annual output, and their
composition is specific: journal articles with a DOI that OpenAlex has not indexed or has indexed under a
different identifier, conference papers mostly without a DOI, which are the hardest to link by title, and
doctoral theses, which DBLP indexes from a few national repositories and OpenAlex largely does not. The
``data'' type, DBLP's record of datasets and software, grows across the window and is almost entirely
unmatched, which is a reminder that the research outputs of computer science that are not papers are
outside the corpus altogether. For 2026 the conference share of the unmatched records rises sharply, which
is the DBLP-side manifestation of the right truncation discussed in Section~\ref{sec:data-dates}: DBLP
indexes a proceedings volume as a whole when it appears, OpenAlex matches it paper by paper over the
following months, and the gap is largest in the most recent year. The missing records bias the indicators
of this part toward the parts of computer science that publish with DOIs in journals and large conference
series, that is, away from theses, workshop papers and national venues; the direction of the bias is known
and its magnitude is bounded by the table.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_dblp_only}\endgroup

\subsection{Why the creation date does not measure indexing lag}

The research plan proposed to estimate the indexing delay of OpenAlex from the \texttt{created\_date} of
each record and to correct the recent months of the publication series for it. Part~III
(Section~\ref{sec:data-dates}) records why the proposal was abandoned; Table~\ref{tab:indexing_lag} gives
the evidence in annual form. For every publication year up to 2024, the median lag between publication and
record creation is of the order of years, it is larger for January than for June publications by almost
exactly five months, and more than nine tenths of the year's records were ``created'' more than 180 days
after publication. A genuine indexing delay cannot have that shape: it would be measured in weeks or
months, would not depend on the month of publication within the year, and would not place nearly all
records beyond the 180-day mark. The shape is that of a single creation date for the bulk of the database,
with the lag equal to the time between each work's publication and that date, which places the date in the
second half of 2025. For works published in 2025 and 2026 the field behaves differently: a large share of
records is created within 90 days of publication, and the median lag collapses to days by mid-2026. The
field therefore measures the delay only for records created after the re-ingestion, and only for them
would a lag profile be meaningful; a profile estimated from the whole table, or from the years that the
structural-change analysis needs for its pre-trend diagnostics, would be an artefact of database
maintenance. This is the reason the structural-change analysis truncates the series rather than correcting
it (Section~\ref{sec:m-truncation}), and it is the reason the only honest estimator of indexing lag is the
comparison of two snapshots of the same database, which the released raw snapshots make possible for a
future study.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_indexing_lag}\endgroup

\section{Hypotheses H4--H6 at this stage}
\label{sec:net-hypotheses}

The protocol states its hypotheses with a direction so that null and opposite results are reported as
such. On the evidence of this part, the verdicts are the following, each limited to the component of the
hypothesis that the available tables test.

H4 (convergence) is not testable in its stated form, which concerns citation flows between areas of the
ontology and the modularity of the area network; those statistics await the classification. Its field-level
counterpart, the share of computer-science references that cross into other OpenAlex fields, is flat over the
window on the v1 graph (Section~\ref{sec:net-flows-fields}), which neither supports nor contradicts the
within-field convergence the hypothesis describes.

H5 (concentration) has two components. The citation-inequality component is stated for AI categories and is
pending; its aggregate counterpart gives a Gini of three-year citations that falls through the baseline and
rises for the one complete post-period cohort, a movement dominated by the share of uncited works and by
right truncation, and therefore not interpretable as a change in concentration. The venue-concentration
component predicted a stable or lower index once preprints are treated separately; the index with arXiv
included rises, for the mechanical reason the protocol anticipated, and the index without the preprint type
is pending. The non-arXiv venue landscape widens.

H6 (geography and collaboration) has three components. The international co-authorship share does not
rise, as predicted, and in fact declines slightly, with a composition explanation that the country shares
support. The China share rises in the aggregate under both counting conventions, as predicted, but as the
continuation of a baseline trend, and the category-specific version is pending. The industry share does
\emph{not} rise in the aggregate: it peaks in 2021 and declines in every post-period year, which is the
opposite of the predicted direction, with the category-specific version pending and with the frontier-level
measures of the literature it was drawn from measuring a different object.

What the part adds beyond the hypotheses is a set of structural observations that were not predicted and
that the pending analyses will have to accommodate: the fall in absolute joint output between China and the
United States during a period in which both grew; the stability of the institutional hierarchy; the rise of
generalist repositories among the largest sources of computer-science records; the steady shift of
references toward younger work without acceleration at the boundary; and the record-level artefacts in the
most-cited lists, which make any ranking of influential works conditional on an audit that this part has
specified but not performed.