% 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/*.csv (corpus v3 graph, 2026-11-03 18:44;
% tables tab_field_flows, tab_reference_coverage, tab_cited_age regenerated from them by tables/make_tables.py, Agent L/M).

\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 (the API increment of
Part~III is archived but not yet merged into the analytical corpus), 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 uses the primary category of Part~IX: Table~\ref{tab:net_category_actors} gives,
for each of the forty categories, the share of works with a China-affiliated author in the baseline and in
the post period, Table~\ref{tab:net_ai_vs_rest} pools the nine categories of the AI/ML area against the
thirty-one others, and Table~\ref{tab:net_ai_vs_rest_yearly} gives the two pooled series by year. Three
things must be said before reading them. The denominator of these shares is every work of the category,
including works without affiliation data, so the level is below that of Table~\ref{tab:country_concentration}
and is depressed wherever affiliation coverage is low, which is the case for the most recent cohorts and for
preprint-heavy categories; the within-category comparison across periods is affected to the extent that
coverage changed. The grouping by primary category assigns a work to one category only, so a vision paper
that uses a language model counts under computer vision, not under large language models. And the AI/ML
area of the ontology is wider than the four categories that define the post period, since it also contains
reinforcement learning, machine-learning theory, deep-learning architectures, agents and AI safety.

With these qualifications, the China share rises from the baseline to the post period in the AI/ML area, as
H6 predicts, and it rises in the pooled other areas as well, by a larger margin; the note of
Table~\ref{tab:net_category_actors} counts the categories in which the share rises, and the rise is close to
universal outside the AI/ML area. Within the AI/ML area the rise is carried by the older categories,
reinforcement learning, deep-learning architectures and agents, while the categories that define the post
period behave differently: the share is nearly flat for large language models, falls for foundation models and
generative AI, and is highest of all forty categories, in both periods, for multimodal AI. The United States
share falls in both groups and in most categories; agents and large language models are the AI/ML
categories in which it rises. The yearly series of Table~\ref{tab:net_ai_vs_rest_yearly} show the pooled
shares of the two groups moving together: both rise through 2023 and fall in 2024 and 2025, and the gap
between them, roughly constant through 2023, closes in 2024 and 2025. The fall after 2023 coincides with the lower
affiliation coverage of recent cohorts (Section~\ref{sec:net-teams}) and cannot be read as a reversal; what
it does establish is that the AI/ML area is not where the China share grows fastest. The verdict on this
component of H6 is therefore a supported direction with an unsupported specificity: the share rises in AI
categories, but less than elsewhere, and the rise is the continuation of a trend that predates the window and
is documented in every recent comparison of national output \citep{bornmann2021growth}.

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
\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_net_category_actors}\endgroup
\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_ai_vs_rest}\endgroup
\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_ai_vs_rest_yearly}\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
Tables~\ref{tab:net_category_actors}, \ref{tab:net_ai_vs_rest} and~\ref{tab:net_ai_vs_rest_yearly} settle it
in the negative. The company share of the AI/ML area is higher than that of the other areas in every year,
which is the familiar result that industry is more present in machine learning than in the rest of computer
science; but it peaks in 2021 and falls in every subsequent complete year, so that the baseline-to-post decline of the
AI/ML area is larger than that of the other areas, not smaller. The note of
Table~\ref{tab:net_category_actors} counts the categories whose company share rises: one of the nine AI/ML
categories (agents), against a sizeable minority of the others, among them cloud computing, information
retrieval, distributed computing, database systems, operating systems and quantum computing. The AI/ML
categories with the highest baseline company shares, multimodal AI, reinforcement learning, foundation
models and large language models, all lose share in the post period, and generative AI loses more than
half of its share. The denominator caveat of the previous paragraph applies with more force here than for the
China share, because the AI/ML area has the highest share of arXiv-linked works
(Table~\ref{tab:net_ai_vs_rest}) and preprints are the records least often enriched with affiliations; part of
the measured decline is therefore coverage. Nothing in the category tables, however, suggests the opposite
sign for the AI categories, and the frontier-share results of \citet{ahmed2023industry} remain the only
sense in which an industry share has risen.

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 slower channels of indexing (and citation extraction) are not complete; 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 in Table~\ref{tab:net_category_gini}, which
gives the Gini of $c^{(36)}$ by primary category for every publication year with a complete window, and in
Table~\ref{tab:net_gini_ai_vs_rest}, which pools the AI/ML area against the other areas as work-weighted means
of the category statistics. Two patterns are visible. Between the 2018 and 2022 cohorts the within-category Gini falls in
almost every category, as the aggregate does, and for the same reason, the falling share of uncited works;
the exceptions are algorithms and large language models.
For the 2023 cohort the pooled AI/ML Gini is above its baseline mean while the pooled Gini of the other
areas is below its own; the note of Table~\ref{tab:net_category_gini} counts the categories whose 2023 value
exceeds their baseline mean, and the proportion is far higher among the AI/ML categories than among the
others. Large language models have the highest Gini of any category in every year from 2019 onward (the
implausible 2023 value of formal verification apart), and theirs ends the baseline above where it began,
which makes it the clearest category-level exception to the baseline decline. This is evidence in the direction of H5, and it is weak evidence: it rests on a single
post-period cohort whose window is affected by truncation, the uncited share of that cohort rises by about
the same amount in both groups, so the difference between them is a tail effect rather than a zeros effect,
and the small categories, together with the implausible 2023 value for formal verification, show the
sensitivity of a within-category Gini to a single misattributed record
(Section~\ref{sec:net-topcited}). The 2024 cohort, whose window closes at the end of 2026, will be the first
test with two post-period cohorts.
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
\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_net_category_gini}\endgroup
\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{2.5pt}\input{tables/tab_net_gini_ai_vs_rest}\endgroup

\subsection{The most cited works and what they reveal about the database}
\label{sec:net-topcited}

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. (This item does not depend on the
classification and remains open; it belongs to the RQ3 human-review checkpoint, not to the corpus pipeline.) 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}. (Also left open: the
category-level mean normalised scores of \texttt{category\_impact\_yearly.csv} are computed on the unaudited
reference classes and are for that reason not reported in this part.)

\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. Figure~\ref{fig:field_inflows} and
Table~\ref{tab:field_flows} are generated from the current graph tables of \texttt{results/graph/}
(\texttt{field\_flows\_yearly.csv}, corpus v3), and Table~\ref{tab:reference_coverage}, from
\texttt{reference\_coverage\_yearly.csv}, gives the denominators on which every share in this section rests:
the declared references of the eligible works of each citing year, the share of them that resolve to an
OpenAlex record, and the split of the resolved references into internal and external edges.

\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 by
\texttt{figures/make\_figures.py} from \texttt{results/graph/field\_flows\_yearly.csv} (corpus v3); the
values are in Table~\ref{tab:field_flows}.}
\label{fig:field_inflows}
\end{figure}

Table~\ref{tab:reference_coverage} is read first because it conditions the rest. The number of declared
references per eligible work rises through the baseline and falls again in the last three citing years, the
2026 row being the shortest; this is the right-truncation of reference lists (recent records are indexed
before their reference lists are complete) rather than a change in citing practice, and it means that the
shares of the last two rows of every table in this section are computed on fewer references per work than
the earlier rows. The share of declared references that resolve to an OpenAlex record is nearly constant
from 2018 to 2024 and higher in 2025--2026; the recent cohorts carry fewer parsed references per work (the
reference-extraction channels of OpenAlex lag publication), and the references that are already parsed for
them resolve more often. The difference describes how the database was assembled, not what authors cite, and
it is the reason the flow statistics are expressed as shares of resolved references, as the methodology requires.
The internal share of resolved references rises steeply with the citing year, and this is the mechanical
feature of Figure~\ref{fig:field_inflows} that must be read before any other: the corpus starts in 2018, so 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 share of references pointing to computer science outside the corpus, which is
mostly pre-2018 computer science, falls as the internal share rises.

The two computer-science columns of Table~\ref{tab:field_flows} do not, however, sum to a constant. Their
sum, the share of references that stay within the field, rises in every citing year of the window, and its
complement, the share of references that cross into another OpenAlex field (column `Other fields'), falls in
every year, in the baseline years as in the post years and at a comparable pace on either side of the 2022
boundary. Engineering, the largest external field, accounts for the greater part of the decline;
mathematics, decision sciences, physics and psychology decline slowly; the social sciences are stable; and
medicine is the only field among the seven whose share rises, so that by the end of the window it is the
second largest external destination after engineering. On this evidence the field-level version of H4 is
not supported: the boundary-crossing share of computer-science references toward other fields does not rise
after 2022, it continues to fall, and no change of pace is visible at the boundary.

Two reservations qualify the direction, though not the absence of a break. The first is a classification
boundary. The eligible corpus is the CS core of Part~III, that is, works with a computer-science topic
whatever their primary field, so a post-2018 engineering work with a computer-science topic is an internal
edge while its pre-2018 counterpart is an external edge typed as engineering; as the corpus lengthens, part
of what used to be counted as a flow to engineering or mathematics is re-counted as internal, and the
decline of the external shares is to that extent mechanical. The field-flow file does not type internal
edges by the cited work's primary field, so the size of this effect cannot be removed here; a flow table
that types every resolved reference, internal or external, by primary field would be the correction, and it
is noted for the director. The second is that H4 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 engineering or mathematics. A falling external share is
therefore compatible with H4 and with its negation, and only the category flow matrices can decide between
them. What the field-level table does establish is a boundary condition for the interdisciplinarity
literature: the diversity indices of Section~\ref{sec:m-diversity}, whether Rao--Stirling or
Leinster--Cobbold, are computed over a reference distribution whose external component is shrinking
smoothly, so that any change they detect at the 2022 boundary 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 columns show
the neighbouring fields (engineering, mathematics, decision sciences) losing share and a non-neighbouring
one (medicine) gaining it, and they do not show the acceleration that the foundation-model narrative would
predict.

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3pt}\input{tables/tab_reference_coverage}\endgroup

\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{2.5pt}\input{tables/tab_field_flows}\endgroup

\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, read
from the corpus v3 file \texttt{results/\allowbreak graph/\allowbreak cited\_age\_yearly.csv}, which is built on the same edge sets as
Table~\ref{tab:reference_coverage}. The mode of citation age is two years in every citing year (visible in
the figure, where every curve peaks at the same abscissa); the mean age falls in every citing year from 2018
to 2026; the median falls over the baseline years and is constant from 2021 onward; the share of
references to works at most five years old rises by roughly the amount by which the share of references to
works more than ten years old falls; and the share of references to works at most two years old rises less,
and mostly during the baseline years. 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, and the year-to-year changes
of the mean in the table are of the same order before and after it, if anything smaller after. 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 to zero over the window as the corpus's own dates
become first-appearance dates, and it 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 by \texttt{figures/make\_figures.py} from
\texttt{results/\allowbreak graph/\allowbreak cited\_age\_yearly.csv} (corpus v3); summary statistics in Table~\ref{tab:cited_age}.}
\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.
Table~\ref{tab:reference_coverage} is the control. The resolved share is nearly constant from 2018 to 2024,
so over those years a resolution bias toward recent works would shift the level of the age distribution but
not its trend; the fall of the mean and of the over-ten-year share between 2018 and 2024 is therefore not an
artefact of a rising resolvable share. The 2025 and 2026 rows are different: their resolved share is higher
and their reference lists shorter (right-truncation), and the small further decline of the mean age in those
two rows should not be read on its own. The age shift is reported here as observed within the resolved
references, not as corrected for the composition of the unresolved ones, which cannot be typed.

\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. They require the primary category of
every work, which the classification of Part~IX supplies, and they are computed by
\texttt{knowledge\_graph/02\_category\_flows.py} on the internal edges of Section~\ref{sec:m-citgraph},
that is, on references from eligible works to eligible works with a primary category at both ends.
Two properties of this edge set govern everything that follows. First, the internal network is small in
2018 and grows with every citing year, because the corpus begins in 2018 and a citing year can only cite
the corpus years that precede it; the 2018 row of every table below describes a network of references to
works of the same year and is not comparable with the later rows, so the series effectively begin in 2019.
Second, the restriction to internal references means that an area's flows are measured over its references
to \emph{recent} computer science only; references to older work and to other fields, which
Sections~\ref{sec:net-flows-fields} and~\ref{sec:net-age} showed to be a declining share, are outside the
matrix. Table~\ref{tab:net_area_flows} and Figure~\ref{fig:area_flow_matrix} give the area flow matrices
by period, Table~\ref{tab:net_category_to_ai} the share of each category's internal references that go to
the nine categories of the AI/ML area, and Table~\ref{tab:net_modularity} and
Figure~\ref{fig:cross_area} the cross-area shares and the modularities by year.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_area_flow_matrix.pdf}
\caption{Citation-flow matrices between the eight areas of the ontology, baseline (citing years
2018--2022) and post (2023--2026) periods: row shares of internal references from the citing area (rows)
to the cited area (columns), per cent. Source: \texttt{results/graph/area\_flows\_yearly.csv}.}
\label{fig:area_flow_matrix}
\end{figure}

The area matrices are diagonal-dominant in both periods: every area but one sends the majority of its
internal references to itself, from about two thirds for the security, software, theory and
computational-science areas to a much higher share for the perception area, which is the largest area and the one whose categories (vision, language, speech,
robotics, interaction, graphics) cite each other most. The largest off-diagonal flows are structural and do
not change between periods: the AI/ML area sends about a third of its references to the perception area,
which is where the application work on vision and language that the machine-learning categories build on
is classified; the security area sends about a sixth of its references to the data and distributed area, the
networks and cloud work that security builds on; and computational science splits its outside references
between AI/ML and perception. What changes between periods is the AI/ML column. The self-share of every
area except perception and hardware falls, and the share of references each area sends to the AI/ML area rises,
the increments being largest for the software area, computational science, security and the data and
distributed area (Table~\ref{tab:net_area_flows}; the post-minus-baseline differences are the subject of
Part~IX). The AI/ML area's own self-share falls as well, in favour of the perception area: the
machine-learning categories cite vision and language work more in the post period than before, which is the
flow one expects when the models of the post period are evaluated on the tasks of those categories. The
perception area is the exception on both counts: its self-share is the same in the two periods and its
share of references to the AI/ML area changes little, so the convergence that the AI/ML column shows is a
convergence of the smaller areas toward AI, not of the largest.

The category-level table (Table~\ref{tab:net_category_to_ai}) tests H4 at the resolution at which it is
stated, since the hypothesis names systems, security and human--computer interaction as the citing fields
that should cite the AI categories more. All three do. The share of references going to the AI/ML area
rises in human--computer interaction, software engineering, cybersecurity, database systems, distributed
computing, computer networks and computer architecture, in each case from the beginning of the window,
and in each case the values of 2024 and 2025 are at or above every baseline value. The timing differs across these
series in a way the hypothesis does not predict. For human--computer interaction the series is nearly flat
through 2023 and rises steeply in 2024, 2025 and the incomplete 2026; for software engineering the rise
begins in 2021 and steepens from 2023; in both the change is concentrated in the second and third
post-period years rather than at the boundary, consistent
with the lag between the appearance of a model and the appearance of empirical work that cites it; for
cybersecurity, database systems and distributed computing the post-period increments continue the baseline
pace; for computer networks and computer architecture the share is the lowest among the systems categories
and its rise is slight. Within the perception area, natural language processing is the category with the
largest post-period change of any in the table: its share of references to the AI/ML area falls from 2018
to 2020, which is the period in which the pre-trained language model became the standard tool of the
category and was cited as NLP work rather than as machine learning, and rises steeply from 2023, as the
large-language-model category (which the ontology places in the AI/ML area) absorbs the work the category
now builds on. Computer vision shows no such rise, which again reflects the classifier's boundary: vision
work citing vision models is a within-category flow. The theory categories rise modestly, and
computational biology and robotics return in the post period to the levels of the earliest, sparse years. These are
flows of references between classified works; they say that the systems, security and interaction
categories build on AI/ML-classified work more than they did, which is what H4 asserts, and not that the
work itself has become AI research, which is a question about classification rather than citation.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.95\textwidth]{fig_cross_area.pdf}
\caption{Left: share of internal references leaving the citing area, $X_{\alpha,t}$ of
equation~\eqref{eq:cross-area}, by citing area and year (per cent). Right: modularity of the yearly
category citation-flow network at the area and category partitions (equation~\eqref{eq:modularity}) and the
within-category self-share. Sources: \texttt{results/graph/cross\_area\_share\_yearly.csv},
\texttt{results/graph/modularity\_yearly.csv}. 2026 is incomplete.}
\label{fig:cross_area}
\end{figure}

The cross-area shares (Figure~\ref{fig:cross_area}, left; the yearly values by area are in Part~IX) order
the areas by how much of their citation leaves them. The AI/ML area has the highest boundary-crossing rate
in every year and the rate rises through 2022 and is flat thereafter; its position at the top is a
consequence of where the ontology draws its boundaries, since the area's two largest partners, vision and
language, are placed in a different area, and the statistic would be lower under any ontology that grouped
machine learning with its application fields. This dependence on the partition is the reason
Section~\ref{sec:m-networks} describes $X_{\alpha,t}$ as a boundary-crossing rate and not as a measure of
interdisciplinarity in the sense of \citet{stirling2007diversity} or \citet{rafols2010diversity}, whose
indicators weight pairs of categories by their distance. The security, software and data areas
rise through the whole window; the theory area rises in the sparse early years, is flat in the late
baseline and rises again in the post period; the hardware area is flat, computational science rises and
falls back in the incomplete year, and the perception area, after a fall in 2019 that belongs to the small
2018 network, is flat at the lowest level. Table~\ref{tab:net_modularity} aggregates these shares over areas
in two ways. The raw aggregate is flat through the baseline and rises in every post-period year; the
composition-adjusted aggregate, which holds the weights of the citing areas at their baseline values, rises
by less, so part of the post-period rise of the raw series is the growing weight among citing works of the
AI/ML area, which is the most boundary-crossing area, and the remainder, which is positive in every
post-period year, is a within-area rise of boundary crossing. H4's first component, that the share of
citations crossing area boundaries rises in the post period, is supported on both the raw and the adjusted
series, with the composition qualification stated.

H4's second component is the modularity. $Q_{\mathrm{cat}}$ peaks in 2019 and falls in every subsequent
year; $Q_{\mathrm{area}}$ falls in every year from 2018 to 2025 and is flat, with a slight uptick in the
incomplete year, from 2023 onward; the self-share peaks in 2019, is nearly flat through 2022 and falls in every post-period year, fastest after 2023
(Table~\ref{tab:net_modularity}, Figure~\ref{fig:cross_area}, right). The post-period means are below the
baseline means at both partitions, as the note of the table records, so the verdict on this component is
that the hypothesis is supported in direction at both levels. The caveats are substantive. The decline is
present throughout the baseline; the 2022 boundary is not a break in either series; the yearly
decrements of $Q_{\mathrm{cat}}$ are somewhat larger in the post period than in the late baseline, while
$Q_{\mathrm{area}}$ stops falling after 2023, so that the two partitions tell different stories about the
post period: continued, slightly faster de-assortment between categories, and an end to the decline between
areas. Because the partition is fixed, a fall in
$Q$ can arise from a change in the mix of citing works as well as from a change in citing behaviour; the
adjusted cross-area series shows that both are present. The modularity of equation~\eqref{eq:modularity}
inherits every property of the classifier, and in particular the placement of large language models in the
AI/ML area and of natural language processing outside it converts the post-period citation of LLM work by
NLP work into a cross-area flow by construction. The internal network grows by an order of magnitude over
the window, so the 2018 and 2019 values describe sparse networks; and the 2026 row is a partial year whose
works carry fewer parsed references. The co-classification matrix of
\texttt{category\_cooccurrence\_yearly.csv}, which counts works carrying two categories in their full label
set, is reported in Part~IX and is not used here, because, as Section~\ref{sec:m-classification} notes, it
responds to abstract length and vocabulary in a way the primary-label flows do not. What the flows and the
modularity together establish is modest and definite: the citation network of recent computer science is
becoming less assortative by category, the change is gradual and began before 2022, and the areas that
have moved are the smaller ones, which cite the machine-learning categories more, while the largest area
cites itself as much as it ever did.

\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_area_flows}\endgroup
\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_modularity}\endgroup
\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_net_category_to_ai}\endgroup

\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 supported in direction on both of its components and qualified on both. The share of
internal references crossing area boundaries rises in the post period, on the raw aggregate and on the
composition-adjusted aggregate alike, and the systems, security and interaction categories the hypothesis
names all send a growing share of their references to the AI/ML categories, with the steepest rises for
human--computer interaction and software engineering in 2024--2026 rather than at the boundary
(Tables~\ref{tab:net_category_to_ai} and~\ref{tab:net_modularity}). The modularity falls at both the
category and the area partition, with post-period means below baseline means, but the fall is a
baseline trend that continues, slightly faster, at the category level and stops at the area level after 2023; part of it is
the growing weight of the most boundary-crossing area among citing works, and all of it depends on where the
ontology draws the boundary between machine learning and its application fields
(Section~\ref{sec:net-flows-categories}). The field-level counterpart, the share of computer-science
references that cross into other OpenAlex fields, falls through the window with no change of pace at the
boundary (Table~\ref{tab:field_flows}, Section~\ref{sec:net-flows-fields}), part of the fall being a
mechanical consequence of the corpus boundary; convergence within computer science and a narrowing of its
references outside computer science are therefore observed together.

H5 (concentration) has two components. The citation-inequality component is stated for AI categories, and
for the one post-period cohort with a complete window the pooled Gini of the AI/ML categories is above its
baseline mean while that of the other categories is below, with most AI/ML categories and a minority of the
others above their baseline means and large language models the most unequal category in every year
(Tables~\ref{tab:net_category_gini} and~\ref{tab:net_gini_ai_vs_rest}); this is the predicted direction, on
one cohort affected by right truncation, with the uncited share rising equally in both groups, so the
evidence is weak and provisional until the 2024 window closes. The aggregate counterpart gives a Gini of
three-year citations that falls through the baseline and rises for that same cohort, a movement dominated by
the share of uncited works and by truncation, and 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; it rises in the AI/ML categories too, by less than in the other categories,
so the specificity the hypothesis asserts is not observed, and the categories that define the post period
(large language models, foundation models, generative AI) are flat or falling
(Tables~\ref{tab:net_category_actors} and~\ref{tab:net_ai_vs_rest}). 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; the category-specific version is also opposite, with the AI/ML area losing more company
share than the other areas and all of its highest-share categories losing share, part of the decline being
the lower affiliation coverage of preprint-heavy categories, 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 interpretation of Part~IX 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; the asymmetry of the category flows,
in which the smaller areas move toward the machine-learning categories while the largest area, perception
and interaction, cites itself as much as before; the late timing of the rise in citation of AI work by
human--computer interaction and software engineering, two to three years after 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.