1% part08_networks.tex — Part VIII, Scientific Knowledge Networks (Agent L/I, 2026-11-03).2% Every corpus number is a macro from tables/numbers.tex or appears in a generated table (tables/make_tables.py).3% Result files: results/bibliometrics/*.csv (corpus v2, 2026-11-03 18:0x) and results/graph/cited_age_yearly.csv (v1, pending v2).45\section{Scope and reading rules}6\label{sec:net-scope}78This part reports what the eligible corpus shows about the people, organisations, countries and venues that9produce computer-science research, about the distribution of attention over the works they produce, and about10the sources on which that research draws. It is the empirical counterpart of research questions RQ4 and RQ611and of the networks section of the methodology (Section~\ref{sec:m-networks}), and it tests the parts of12hypotheses H4, H5 and H6 that the current result files make testable. The citation-flow statistics between13taxonomy categories, which carry the main weight of H4, depend on the classification of Part~IX and are not14yet available; Section~\ref{sec:net-flows-categories} is a placeholder for them. The reader should15therefore expect a part that is complete on collaboration, geography, institutions, venues and aggregate16citation structure, and provisional on knowledge flows.1718Three reading rules apply throughout. First, every indicator is computed on the eligible corpus defined in19Part~III (Section~\ref{sec:data-eligibility}), so that ``computer science'' means the union of DBLP-indexed,20OpenAlex-primary-field and arXiv \texttt{cs} works after the exclusions of the PRISMA flow, and the indicators21inherit the boundary decisions and the affiliation completeness of that corpus. Second, the two periods of the22protocol are unequal in length and in completeness: the baseline runs from January 2018 to the end of23November 2022, the post period from December 2022 to the snapshot of October 2026 completed by the API24increment, and the last year of the post period is partial for the reasons set out in25Section~\ref{sec:data-dates}. Tables by year therefore carry 2026 as an incomplete row, and the fixed-window26citation statistics of Section~\ref{sec:net-citations} are complete only up to the publication years flagged in27Table~\ref{tab:citation_windows}. Third, the comparison of periods is descriptive. The protocol states the28hypotheses with a direction so that null and opposite results can be reported as such, and several of the29results below are of that kind; none of them is evidence of an effect of any single event, and the language of30this part is deliberately that of association and composition.3132The part is organised from the smallest unit of production outward. Section~\ref{sec:net-teams} describes33authorship and team structure; Section~\ref{sec:net-international} the international co-authorship network;34Section~\ref{sec:net-geography} the geography of output; Section~\ref{sec:net-institutions} institutions and35sectors, including the industry share that H6 concerns; Section~\ref{sec:net-venues} publication channels and36venue concentration; Section~\ref{sec:net-citations} the distribution of citations and its inequality;37Section~\ref{sec:net-flows} the inflows of knowledge from other fields and the age of the works cited;38Section~\ref{sec:net-boundaries} the boundary of the database itself, through the DBLP-only records and the39\texttt{created\_date} diagnostic; and Section~\ref{sec:net-hypotheses} collects the verdicts on H4--H6.4041\section{Authorship and team structure}42\label{sec:net-teams}4344The long-run growth of team size in science is one of the most replicated findings of scientometrics:45\citet{wuchty2007teams} documented the shift from solo to team production across fields over five decades,46\citet{lariviere2015teamsize} extended the series back to 1900 and showed that the citation advantage of teams47has grown with it, and \citet{milojevic2014teams} proposed a generative account in which a core of small,48``Poisson-like'' teams coexists with an expanding tail of large ones. Computer science has long been a field of49small teams by the standards of the laboratory sciences, which is why the question for this corpus is not50whether teams grow but whether the rate of growth or the shape of the distribution changes across the 202251boundary. The hypothesis set of the protocol does not take a position on team size, and the evidence is52reported for its own sake and as a control for the collaboration indicators that follow.5354Table~\ref{tab:collaboration} gives the annual series, and Figure~\ref{fig:collaboration} plots the mean and the55tail shares. The mean number of authors per eligible work rises from56\VolumeYearlyTwoZeroOneEightMeanAuthors{} in 2018 to \VolumeYearlyTwoZeroTwoTwoMeanAuthors{} in 2022 and57\VolumeYearlyTwoZeroTwoFiveMeanAuthors{} in 2025, a monotone increase at a pace that does not visibly change at58the boundary; the median stays at three authors in every year, so the growth of the mean is a growth of the59upper tail. The tail shares in the table make the same point: the share of works with five or more authors60rises steadily, and the share with ten or more, although small, roughly triples over the window. The61single-author share falls through 2022 and then rises again, sharply in 2025 and 2026. That reversal is not a change in62research practice. The column of works without any resolved country shows the same U-shape, and the63single-author and unaffiliated shares move together because the records that enter the corpus fastest after64publication (preprints, repository deposits, records not yet enriched with affiliations) are also those whose65authorship metadata is least complete; as those records are enriched and matched to their published versions66in later snapshots, both shares fall. The 2025 and 2026 rows of Table~\ref{tab:collaboration} must therefore67be read as a snapshot of the indexing process as much as of authorship, and the pre-2024 trend is the only68part of the series on which a substantive statement rests.6970\begin{figure}[htbp]71\centering72\includegraphics[width=0.95\textwidth]{fig_collaboration.pdf}73\caption{Team size, international co-authorship and industry participation by year. Mean authors per work and74tail shares from \texttt{team\_size\_yearly.csv}; the international share is the ICS of Part~IV (works with75two or more countries among works with at least one); the company share is over works with at least one76typed affiliation (\texttt{industry\_share\_yearly.csv}). 2026 is incomplete.}77\label{fig:collaboration}78\end{figure}7980\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_collaboration}\endgroup8182The multi-institution share, the fraction of works whose authors list more than one distinct institution,83follows the mean team size through 2022 and then declines, with the same affiliation-completeness84explanation as the single-author reversal: an unaffiliated record cannot be multi-institutional. Here the85substantive literature gives a reason to expect genuine growth. \citet{jones2008multiuniversity} showed that86multi-university collaboration had become the fastest-growing form of team production in the United States,87with a citation premium concentrated in the top-tier institutions, and \citet{adams2013fourthage} argued88that a ``fourth age'' of research organised around international networks of elite institutions was89displacing the national systems of the previous one. The corpus is consistent with continued growth of90multi-institution work up to the point where the affiliation data become unreliable and is silent beyond it.9192Two cautions apply to all of these shares, and they are not specific to this corpus. The first is that93OpenAlex author counts are taken from the authorship lists of the surviving record after deduplication94(Section~\ref{sec:m-dedup}); where a preprint and its published version differ in author list, the published95version wins, which is the appropriate choice but one that makes the count depend on the linkage. The second96is that very large author lists in computer science come disproportionately from a few genres, namely97consortium reports, shared-task overviews and large model ``technical reports'', so that the ten-plus share98measures the prevalence of those genres as much as the size of ordinary research teams. The disruption99literature attaches a substantive interpretation to team size, with \citet{wu2019disruption} reporting that100small teams produce more disruptive work and large teams more developmental work; that interpretation is101not tested here, because the disruption index requires a citation graph with a long post-publication horizon102that the post period does not yet provide.103104\section{International co-authorship}105\label{sec:net-international}106107International collaboration has grown in every field and every country for which long series exist108\citep{wagner2015cooperation, wagner2017collaboration}, and the growth has been described as the emergence109of a self-organising global network with a core group of countries that is stable over time110\citep{leydesdorff2008core}. The protocol's H6 predicts, against this background, that the international111co-authorship share of computer science does \emph{not} rise in the post period. The prediction was motivated112by two considerations stated in the protocol discussion: the geopolitical restriction of some113bilateral channels after 2020, and the shift of a growing share of the field's output into114preprint channels and into countries whose output is predominantly domestic.115116The international collaboration share (ICS, Section~\ref{sec:m-bibliometrics}) is computed among works with117at least one resolved country, so that the affiliation-completeness problem of the previous section does not118enter the denominator. Its yearly values are in the last column of Table~\ref{tab:collaboration} and are119macro-reported here for the end points: \InternationalCollabYearlyTwoZeroOneEightShareIntl{} in 2018,120\InternationalCollabYearlyTwoZeroTwoZeroShareIntl{} in 2020, \InternationalCollabYearlyTwoZeroTwoTwoShareIntl{}121in 2022, \InternationalCollabYearlyTwoZeroTwoFourShareIntl{} in 2024 and122\InternationalCollabYearlyTwoZeroTwoFiveShareIntl{} in 2025. The series is flat to slightly declining: it123peaks in 2020, is lower in every subsequent year, and the post-period values are below every baseline value.124The null part of H6 is therefore supported in the direction stated, and the result is in fact stronger than125the hypothesis, which only predicted the absence of a rise. Two qualifications prevent a stronger reading.126The denominator grows faster than the numerator over the window127(\InternationalCollabYearlyTwoZeroOneEightN{} works with a country in 2018 against128\InternationalCollabYearlyTwoZeroTwoFiveN{} in 2025), and the composition of that growth, examined in the next129section, is dominated by countries with low international shares; a constant propensity to collaborate within130every country would produce exactly this aggregate decline. And the share is a share of works, not of131authors or of citations, so that the increasing size of international teams noted by132\citet{wagner2017collaboration} would not register in it.133134The 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 works135in a period. The threshold is a reporting choice (Section~\ref{sec:m-bibliometrics}); it keeps the network to136the pairs whose weight is robust to small linkage errors, at the cost of excluding the long tail of weak ties137through which, in the account of \citet{leydesdorff2008core}, peripheral countries enter the core. On this138restricted network, the number of edges and the number of countries both increase from the baseline to the139post period even though the post period is about ten months shorter, so the network densifies at the140threshold. The ordering of countries by strength, the sum of a country's edge weights, changes at the top:141the United States has the largest strength in the baseline and China in the post period, with the United142Kingdom third in both. The twenty strongest pairs (Table~\ref{tab:country_pairs}) show where the change comes143from. The China--United States pair is the heaviest edge in both periods, but its weight is lower in the post144period than in the baseline in absolute terms, while the pairs of China with Hong Kong, Singapore, the United145Kingdom and Australia rise in weight, and Hong Kong and Singapore rise in rank; the China--Hong Kong pair146moves from fourth to second.147The share of the China--United States edge in the total weight of the network falls accordingly148(Table~\ref{tab:country_network}). A decline in the absolute volume of joint work between the two largest149producers, in a period in which the output of both grew, is the most distinctive structural feature of the150collaboration data, and it is consistent with the bilateral-restriction channel that motivated H6; it is151not, on its own, evidence about the cause, and the reader should note that Hong Kong and Macau carry their152own country codes in OpenAlex, so that part of the apparent reorientation of China's collaboration is a153reorientation toward its own special administrative regions.154155Most of the rest of the pair table is continuity. The United Kingdom--United States, Germany--United156States and Germany--United Kingdom pairs keep approximately their weights; the India--United States pair157rises; the Canada--China and Canada--United States pairs fall slightly; and the France--United States and158Australia--United States pairs fall more and drop in rank, two movements that the table records and this159part does not explain. The picture is that of a core group whose composition is stable, as160\citet{leydesdorff2008core} and \citet{glanzel2001national} found for science as a whole, with one edge161weakening and a cluster of East-Asian edges strengthening. Degree-based statistics of the network162(density, clustering, assortativity) are not reported, because at a fixed weight threshold they measure163the growth of the corpus as much as the structure of collaboration; the strength ordering and the pair164weights, which are counts, are the statistics that survive that objection.165166\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_country_network}\endgroup167\input{tables/tab_country_pairs}168169\section{The geography of production}170\label{sec:net-geography}171172The country-level composition of output is the part of this study where the counting convention matters173most, and the methodology (Section~\ref{sec:m-bibliometrics}) reports both. Under full counting a work with174authors in three countries is counted once for each; under fractional counting it is divided among them.175The two conventions give different levels, and the difference is itself informative, because a country whose176full-count share is much larger than its fractional share is one whose output is predominantly177collaborative \citep{gauffriau2008counting, waltman2015counting}. Table~\ref{tab:countries} gives the178fractional counts of the fifteen largest countries by year, Table~\ref{tab:country_shares} the corresponding179shares, Table~\ref{tab:country_concentration} the concentration of the distribution and the full-count shares180of the two largest producers, and Figure~\ref{fig:country_shares} the shares of the eight largest.181182\begin{figure}[htbp]183\centering184\includegraphics[width=0.95\textwidth]{fig_country_shares.pdf}185\caption{Country shares of eligible output under fractional counting, eight largest countries by cumulative186output. Each work is divided equally among its distinct author countries; works without a resolved country187are excluded. Source: \texttt{results/bibliometrics/countries\_yearly.csv}. 2026 is incomplete.}188\label{fig:country_shares}189\end{figure}190191The dominant movement is the rise of China's share, which is already the largest in 2018 and grows in every192complete year of the window, under both counting conventions. The second is the decline of the United193States' share, which is monotone through 2025 under both conventions and recovers only in the incomplete1942026 row, where the fast channels in which American output is over-represented (preprint servers) weigh more195than they will once the year is fully indexed. The third is the growth of India and, more sharply in196relative terms, Indonesia, which enters the top five by the end of the window; the fourth is the slow197relative decline of the large European producers, Japan and Korea, whose absolute output is flat or rising198(Table~\ref{tab:countries}) while the total grows. The Russian series falls after 2021 and does not199recover. These movements are gradual and are visible in the baseline as well as in the post period;200nothing in the country shares changes direction at the 2022 boundary, and the growth of China's share is201if anything slower in 2024 and 2025 than in 2021 and 2022.202203The China part of H6 asks whether the share of works with China-affiliated authors rises in the post period204\emph{in the AI categories}. The aggregate rise is established by Table~\ref{tab:country_concentration},205whose column of works with a China-affiliated author is the quantity the hypothesis names; the category-specific version requires the206classification and is \pending{China share by category after classification}. The aggregate result is,207however, weaker evidence than it looks, because the rise is a continuation of a trend that predates the208window and is documented in every recent comparison of national output209\citep{bornmann2021growth}; a test of H6 that would be informative must compare the post-period210growth of China's share in AI categories with its growth in the rest of computer science, which is what the211pending analysis will do.212213Concentration across countries, measured by the Herfindahl--Hirschman index of fractional shares and by the214shares of the five and ten largest countries, rises through 2025 (Table~\ref{tab:country_concentration}).215The index is dominated by the largest share, so the rise is mostly China's rise; the top-ten share moves216less than the top-five share, which means that the countries ranked six to ten lose share to those ranked217one to five rather than to the tail. The number of countries with any output is stable. The widely218discussed concern that the geography of AI research is narrowing \citep{klinger2020narrowing,219ahmed2020dedemocratization} is a concern about institutions and compute rather than about countries, and the220country-level concentration measured here speaks to it only indirectly; the institutional evidence is in the221next section.222223The ratio of a country's full count to its fractional count, in the last two columns of224Table~\ref{tab:country_concentration}, exceeds one by the extent to which its works are co-authored with225other countries, and it is informative about collaboration intensity. China's ratio is lower than the United226States' in every year, which is the signature of a more domestic output: a larger fraction of227Chinese-affiliated works has only Chinese affiliations. Since China's share grows and the228United States' falls, the aggregate international share of Section~\ref{sec:net-international} is pulled229down by composition even if no country's propensity to collaborate changes. This is the mechanical230channel behind the null result on international collaboration, and it is the reason that result is231reported with the composition caveat rather than as a change in behaviour.232233\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_countries}\endgroup234\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_country_shares}\endgroup235\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_country_concentration}\endgroup236237\section{Institutions and sectors}238\label{sec:net-institutions}239240\subsection{The sectoral mix of affiliations}241242OpenAlex types every institution as education, facility, company, government, healthcare, nonprofit,243funder, archive or other. Table~\ref{tab:institution_types} gives the distribution of typed affiliations over244these classes by year, and Table~\ref{tab:industry} the share of works with at least one company affiliation,245which is the statistic named by H6. The hypothesis predicts that the industry share rises in the post period246in AI categories. The prediction follows a line of work that has documented the growing weight of industry in247machine-learning research: \citet{frank2019citationgraphs} traced the shift of the AI citation graph toward248industry-authored and computer-science-internal sources, \citet{ahmed2023industry} reported that industry's249share of the largest models, of the most cited papers and of the field's PhD graduates had risen sharply in250the decade to 2022, and \citet{klinger2020narrowing} argued, in a preprint, that the thematic diversity of AI251research had narrowed as the private sector's share rose.252253The aggregate corpus does not show a rising industry share. The company share of works with a typed254affiliation is \IndustryShareYearlyTwoZeroOneEightShareCompany{} in 2018, rises to a maximum of255\IndustryShareYearlyTwoZeroTwoOneShareCompany{} in 2021, and then falls in every subsequent year to256\IndustryShareYearlyTwoZeroTwoFiveShareCompany{} in 2025, which is below the 2018 value; the incomplete2572026 row is at \IndustryShareYearlyTwoZeroTwoSixShareCompany{}. The absolute number of works with a company258affiliation keeps growing (\IndustryShareYearlyTwoZeroOneEightNCompany{} in 2018 against259\IndustryShareYearlyTwoZeroTwoFiveNCompany{} in 2025), so the falling share is a matter of the denominator260growing faster: the growth of the post-period corpus comes disproportionately from education-sector output,261and within that from the countries of Section~\ref{sec:net-geography} whose output is almost entirely262academic. Table~\ref{tab:institution_types} shows the same thing from the other side, with the education263share of affiliations rising through the window and the facility, government and company shares all giving264way. The aggregate part of H6 is therefore not supported; the sign is opposite to the one predicted. Whether265the category-specific version holds, that is, whether the company share rises within the AI categories while266falling in the aggregate, is exactly the kind of composition question that the aggregate cannot settle, and it267is \pending{industry share by category after classification}.268269The result is less at odds with the cited literature than it seems, for three reasons that matter for its270interpretation. \citet{ahmed2023industry} measure industry's presence at the frontier---the largest models,271the most cited papers, the leading conferences---and not its share of all output; a sector can dominate the272frontier of a field while its share of the field's total publications falls, and the two facts are compatible273with a frontier that is increasingly expensive to reach \citep{ahmed2020dedemocratization}. Second, the274OpenAlex institution type is assigned to the institution, not to the author's role, so a work by a275corporate research laboratory published with an academic co-author counts as both, and the share reported276here is the share of works with \emph{any} company affiliation, which is the most inclusive definition.277Third, the affiliation completeness problem of Section~\ref{sec:net-teams} affects the typed denominator:278records without affiliation data are excluded, and if industry-authored preprints are less often enriched279with affiliations than journal articles, the company share of recent years is understated. None of these280reasons reverses the aggregate finding, but together they confine it to what it measures.281282\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_industry}\endgroup283\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_institution_types}\endgroup284285\subsection{Institutional concentration and stability}286287The institution tables (Tables~\ref{tab:institution_concentration} and~\ref{tab:top_institutions}) list288institutions with at least two hundred works in a period, identified by their OpenAlex identifiers only; the289result files do not carry institution names, and this part refrains from resolving the identifiers by hand so290that every statement remains reproducible from the released artefacts. The number of institutions above the291threshold rises from the baseline to the post period, as does the number of works they account for, in both292counting conventions. The ratio of full to fractional counts among the largest institutions is close to two,293meaning that the average work of a large institution carries about one other institution, which is the294multi-institution pattern of Section~\ref{sec:net-teams} seen from the institution's side.295296Concentration among the listed institutions is low and stable: the ten largest account for a few per cent of297the listed fractional output and the hundred largest for less than a quarter, with both shares slightly298higher in the post period. This is a different picture from the one that the concern over the299``de-democratisation'' of AI research conveys \citep{ahmed2020dedemocratization}, and the difference is again300one of object: the distribution of \emph{all} computer-science output over institutions is wide, whereas the301distribution of the frontier of one sub-area may be narrow, and only the latter has been claimed to be302narrowing. The rank stability of institutions across periods is high: of the institutions listed in the303baseline, the great majority are also listed in the post period, and the Spearman correlation of their304fractional counts across the two periods, given in the note to Table~\ref{tab:institution_concentration}, is305close to nine tenths. Among the institutions listed in both periods, the twenty-five largest of the post period306(Table~\ref{tab:top_institutions}) have post-to-baseline ratios that cluster around or somewhat above the307ratio of the two periods' listed totals, with a few institutions growing considerably faster and two of the308largest full-count producers growing slower than the corpus. The institutional hierarchy of computer science, in other words, was not reshuffled in the309post period; it grew in place.310311\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_institution_concentration}\endgroup312\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_top_institutions}\endgroup313314\section{Publication channels and venue concentration}315\label{sec:net-venues}316317The venue is the unit at which the publishing system intersects the research system, and the two have been318changing in opposite directions in computer science for two decades: the publishing side has consolidated319into a small number of commercial and society publishers \citep{lariviere2015oligopoly}, while the research320side has moved a growing share of its first dissemination to arXiv321\citep{sutton2017arxivcs, lin2020arxivcs, lariviere2014arxiv}. The OpenAlex notion of source, on which the322tables of this section are built, follows the venue (a journal, a conference series, a book series, a323repository, an ebook platform) rather than the publisher, so what is measured here is concentration over324venues, and arXiv counts as one venue. The protocol's H5 anticipated this when it predicted that venue325concentration would be ``stable or lower because of preprint growth'' once the preprint source is treated326separately; the methodology (Section~\ref{sec:m-bibliometrics}) notes that the index with arXiv included327rises mechanically with preprint growth.328329Table~\ref{tab:venue_hhi} and Figure~\ref{fig:venue_concentration} give the yearly number of distinct sources,330the Herfindahl--Hirschman index over sources and the share of the largest source. The number of distinct331sources rises every complete year, from \VenueHhiYearlyTwoZeroOneEightNSources{} in 2018 to332\VenueHhiYearlyTwoZeroTwoFiveNSources{} in 2025, so the venue landscape is widening in the sense of variety.333The index, however, rises as well: from \VenueHhiYearlyTwoZeroOneEightHhi{} in 2018 to334\VenueHhiYearlyTwoZeroTwoFiveHhi{} in 2025 and \VenueHhiYearlyTwoZeroTwoSixHhi{} in the incomplete 2026335row, and the share of the largest source, which is arXiv in every year, goes from336\VenueHhiYearlyTwoZeroOneEightTopOneShare{} to \VenueHhiYearlyTwoZeroTwoFiveTopOneShare{} and then to337\VenueHhiYearlyTwoZeroTwoSixTopOneShare{} in 2026. The index is small in absolute terms (its upper bound is338one, reached when a single venue carries all works), and the squared share of arXiv accounts for most of it339in the later years; the 2026 value is an artefact of right truncation, since preprints are indexed within340days and journal and conference records months later (Section~\ref{sec:data-dates}), and will fall as the341year completes. The concentration result is therefore the one the protocol expected in mechanism and the342opposite of the one it expected in sign: concentration over venues, with arXiv counted as a venue, rises343because of preprint growth, and the version of the index without the preprint type, which H5 names, is344\pending{venue HHI excluding preprints}. The qualitative conclusion that does not depend on it is that the345rest of the venue landscape is not concentrating: the number of venues grows, and the second-ranked sources346in Table~\ref{tab:top_sources} hold shares that are an order of magnitude below arXiv's.347348\begin{figure}[htbp]349\centering350\includegraphics[width=0.95\textwidth]{fig_venue_concentration.pdf}351\caption{Number of distinct sources per year (left) and venue concentration (right): Herfindahl--Hirschman352index over sources, scaled by $10^4$, and share of the largest source, which is arXiv in every year.353Source: \texttt{results/bibliometrics/venue\_hhi\_yearly.csv}. 2026 is incomplete and inflated by the354faster indexing of preprints.}355\label{fig:venue_concentration}356\end{figure}357358Tables~\ref{tab:source_types} and~\ref{tab:top_sources} describe the channels themselves. By source type,359journals carry about half of the listed works in both periods, conferences between a fifth and a quarter,360and repositories rise from about an eighth to about a fifth between the baseline and the post period, at361the expense of conferences, book series and ebook platforms. The twenty largest sources make the composition concrete. arXiv362is first in both periods and more than doubles its count; Lecture Notes in Computer Science is second in both;363SSRN, which is not a computer-science venue but hosts a growing number of works that OpenAlex classifies in the364field, moves from the lower part of the baseline list to third; Research Square and NeurIPS enter the365post-period list and the AAAI conference proceedings rise within it; the large open-access366journals (IEEE Access, Sensors, Remote Sensing) remain in the list but with lower counts in the post period367than in the baseline, a decline whose cause (editorial policy, reclassification by OpenAlex, or the shorter368period) the corpus does not identify. The369appearance of generalist repositories (SSRN, Research Square, OSF) among the largest computer-science370sources is a boundary effect of the OpenAlex topic classification rather than a change in where computer371scientists publish, and it is one of the reasons the strict-core sensitivity set of Part~III exists.372373\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_venue_hhi}\endgroup374\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_source_types}\endgroup375\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_top_sources}\endgroup376377\section{The distribution of citations}378\label{sec:net-citations}379380\subsection{Levels, zeros and inequality within fixed windows}381382Citation distributions are heavy-tailed in every field, and the degree of skewness is remarkably similar383across fields once counts are normalised by the field mean \citep{seglen1992skewness, radicchi2008universality,384albarran2011skewness}. The mechanisms proposed for the tail are cumulative advantage, the ``Matthew effect''385by which recognised work attracts recognition \citep{merton1968matthew, price1976cumulative}, and its386network formalisation as preferential attachment \citep{barabasi1999scaling}; the mechanism proposed for the387mass of the distribution is a combination of a work's intrinsic fitness and an ageing function388\citep{wang2013longterm}. What a cross-period comparison can measure is not these mechanisms but the shape389of the distribution at a fixed exposure, and the fixed windows of Section~\ref{sec:m-citations} are the device390that makes the shape comparable: $c^{(36)}$ counts the citations received in the publication year and the two391following calendar years, and is complete for publication years up to 2023.392393Table~\ref{tab:citation_windows} and Figure~\ref{fig:citation_inequality} give the yearly statistics. The mean394of $c^{(36)}$ rises from \CitationWindowsYearlyTwoZeroOneEightMeanCThreeSix{} for works published in 2018 to395\CitationWindowsYearlyTwoZeroTwoTwoMeanCThreeSix{} for 2022 and396\CitationWindowsYearlyTwoZeroTwoThreeMeanCThreeSix{} for 2023, the last complete year; the median is one397citation in most years and two in 2022, so the mean is carried by the tail. The share of works uncited at398three years falls from \CitationWindowsYearlyTwoZeroOneEightShareUncitedThreeSix{} for 2018 to399\CitationWindowsYearlyTwoZeroTwoTwoShareUncitedThreeSix{} for 2022 and rises again to400\CitationWindowsYearlyTwoZeroTwoThreeShareUncitedThreeSix{} for 2023. Both movements are what a growing401citing population produces: each publication year is cited by the following two years' output, and that output402grows, so later cohorts receive more citations at equal exposure \citep{bornmann2015growth}. The reversal in4032023 is the first sign of right truncation in the window, since the third calendar year of the 2023 cohort404is 2025, for which the increment of Part~III is complete but the slower channels of indexing are not; it is405flagged in the table and is the reason the 2024 row, whose window is formally incomplete, is not used.406407The Gini coefficient of $c^{(36)}$ is the inequality statistic named, with a deviation in window length408recorded in Section~\ref{sec:m-bibliometrics}, by H5. It falls from409\CitationWindowsYearlyTwoZeroOneEightGiniCThreeSix{} for 2018 to410\CitationWindowsYearlyTwoZeroTwoTwoGiniCThreeSix{} for 2022, then rises to411\CitationWindowsYearlyTwoZeroTwoThreeGiniCThreeSix{} for 2023; the 12-month Gini follows the same path at a412slightly higher level, as expected from the larger share of zeros in the shorter window. Since the share of413uncited works moves with the Gini, and uncited works are the main contributor to inequality in a short window414(Section~\ref{sec:m-bibliometrics}), the fall through 2022 is to a large extent a fall in the share of zeros415rather than a change in the shape of the tail, and the 2023 uptick is the truncation effect just described.416H5 predicts that citation inequality is higher in the post period than in the baseline \emph{for AI417categories}. The aggregate series can test only the aggregate statement, and for the one post-period418publication year with a complete window (2023) the aggregate Gini is above the 2022 value and below every419baseline value before 2021, so the aggregate evidence is mixed and dominated by truncation; the category420version of the test, which is the one the hypothesis states, is \pending{Gini by category after classification}.421The reader should also weigh the finding of \citet{nielsen2021inequality} that global citation inequality has422risen over several decades when measured on long windows across all fields; the three-year windows used here423measure a different quantity, early attention, whose inequality is driven by zeros, and the two results are424not in contradiction.425426\begin{figure}[htbp]427\centering428\includegraphics[width=0.95\textwidth]{fig_citation_inequality.pdf}429\caption{Fixed-window citation levels and inequality by publication year, for years with a complete43036-month window. Left: mean $c^{(36)}$ and the 99th percentile divided by ten. Right: Gini coefficient of431$c^{(36)}$ and share of works uncited at 36 months. Source:432\texttt{results/bibliometrics/citation\_windows\_yearly.csv}.}433\label{fig:citation_inequality}434\end{figure}435436The field-weighted citation impact supplied by OpenAlex, reported for comparison in437Table~\ref{tab:citation_windows}, has a mean above one in every year, which says that the eligible corpus is438cited above the OpenAlex world average for works of the same type, year and subfield; its median is below439one in every year, which says that the typical computer-science work is not. The two statements together440are the skewness result once more. The mean FWCI declines slowly, though not monotonically, across cohorts and the median rises through4412022 and collapses for 2025 and 2026, where the exposure is too short for the indicator to mean anything;442the methodology's reservations about FWCI (Section~\ref{sec:m-bibliometrics}) are borne out and the443indicator is not used further.444445\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_citation_windows}\endgroup446447\subsection{The most cited works and what they reveal about the database}448449Table~\ref{tab:top_cited} lists the ten works with the largest $c^{(36)}$ in each publication year from 2018450to 2025, with their total citations to date. The list is reported because research question RQ3 asks for the451most influential contributions and because the mandate requires that the manuscript identify them; it is452reported with its errors visible because the errors are instructive. Three kinds of entry appear. The first453is the expected one: the foundational works of the deep-learning decade are present with the citation counts454one would expect, among them \emph{Deep Contextualized Word Representations}, \emph{MobileNetV2} and455\emph{Squeeze-and-Excitation Networks} for 2018, \emph{BERT} for 2019, \emph{Momentum Contrast} and456\emph{A Simple Framework for Contrastive Learning} for 2020, the \emph{Vision Transformer} and the457\emph{Swin Transformer} for 2021, \emph{High-Resolution Image Synthesis with Latent Diffusion Models} and458\emph{Masked Autoencoders Are Scalable Vision Learners} for 2022, \emph{Segment Anything} and459\emph{YOLOv7} for 2023, and \emph{DeepSeek-R1} for 2025, together with the scientific-software and460bioinformatics-resource papers (SciPy, NumPy, STRING, SWISS-MODEL, iTOL, AlphaFold Protein Structure461Database, UniProt, KEGG) that the OpenAlex topic classification places in computer science and that are462among the most cited works of any field.463464The second kind of entry is a duplicate or misdated record of a canonical work: \emph{Bitcoin: A Peer-to-Peer465Electronic Cash System} appears as an SSRN record dated 2019 and again dated 2022, \emph{Generative466Adversarial Nets} as a 2023 book chapter, \emph{Batch Normalization} as a 2024 preprint, \emph{Learning467Multiple Layers of Features from Tiny Images} as a 2024 article, and \emph{Attention Is All You Need} as a 2025468preprint. These are not errors of this study's deduplication, which merges a preprint with its published469version within the window (Section~\ref{sec:m-dedup}); they are distinct OpenAlex works, with their own470identifiers and their own citation counts, created when a reference string resolved to a new record rather471than to the existing one, and dated by the record rather than by the work. Their $c^{(36)}$ is large because472the citations of a canonical work accrue to whichever record the citing works' reference strings resolve to.473The third kind is the inconsistent record: entries whose window count exceeds their total count, or whose474total count is zero while their window count is in the thousands, including several records of the Dagstuhl475DROPS series and of regional journals whose titles bear no relation to the citation volume attached to476them. These are, to the best of the author's understanding, artefacts of OpenAlex's reference matching,477where a frequently cited string has been mapped to a wrong target; they are recognisable precisely because478the two counts disagree, and \citet{alperin2024openalex} and \citet{culbert2025openalexcoverage} document479related inconsistencies in OpenAlex citation data at the aggregate level.480481The consequences for this part are limited but must be stated. The aggregate citation statistics of the482previous subsection are insensitive to a small number of misattributed records among hundreds of483thousands per year, except through the maximum and the 99th percentile, which Table~\ref{tab:citation_windows} reports and484which should not be interpreted. The identification of the most influential works for RQ3, by contrast,485cannot rely on a ranked list from the database without a record-level audit, and the audit must check the486consistency of window and total counts, the uniqueness of the work across records, and the agreement of the487record's date with the work's first appearance. That audit is part of the human-review checkpoint on RQ3 and488is \pending{record-level audit of the top-cited lists}; until it is done, the titles above are quoted as what489the database returns, not as a ranking endorsed by this study. The lesson for the field-normalised scores490of Section~\ref{sec:m-citations} is the same as the one \citet{waltman2016review} draw for all mean-based491indicators: a reference class containing one record with tens of thousands of misattributed citations has a492mean that is wrong for every work in the class, and the normalised scores of Part~IX should be computed493after the exclusion of records failing the consistency check; whether the current pipeline applies that494exclusion is \pending{NCS computed after exclusion of inconsistent records}.495496\begingroup\footnotesize\setlength{\tabcolsep}{4pt}\input{tables/tab_top_cited}\endgroup497498\section{Knowledge inflows and the age of cited work}499\label{sec:net-flows}500501\subsection{Where the references of computer science point}502\label{sec:net-flows-fields}503504Research question RQ4 asks how citation networks and interdisciplinary knowledge flows have evolved, and505H4 predicts that the share of citations crossing area boundaries rises in the post period. The methodology506defines two levels at which flows are measured: between the taxonomy categories of this study, through the507flow matrices of equation~\eqref{eq:flow}, and between the corpus and the rest of the literature, through the508external edge set of Section~\ref{sec:m-citgraph}, whose cited works are typed by their OpenAlex field. Only509the second level is available at the time of writing, and only from the first version of the corpus: the510graph tables of \texttt{results/graph/} are being regenerated for corpus v2, and the field-flow file was not511present when this part was written. Figure~\ref{fig:field_inflows}, generated from the v1 file, is512described here qualitatively, and every quantitative statement about it is \pending{v2 graph}.513514\begin{figure}[htbp]515\centering516\includegraphics[width=0.95\textwidth]{fig_field_inflows.pdf}517\caption{Share of the resolved references of eligible works, by citing year, that point to works inside the518corpus and to works outside it by cited OpenAlex field (seven largest external fields). Generated from the519corpus v1 file \texttt{results/graph/field\_flows\_yearly.csv}; to be regenerated for v2.}520\label{fig:field_inflows}521\end{figure}522523The figure separates the references of each citing year into those that point inside the corpus, that is, to524computer-science works published from 2018 onward, and those that point outside it, by the cited work's525field. Its dominant feature is mechanical and must be read first: the share of references pointing inside the526corpus rises steeply with the citing year, and the share pointing to computer science outside the corpus527falls by the same amount, because the corpus starts in 2018 and a work published in 2018 cannot cite inside528it except at age zero, whereas a work published in 2026 has eight years of corpus to cite. The two529computer-science curves together are approximately flat, and their sum is the share of references that530stay within the field. The curves of the other fields are what the flow question is about, and they are531nearly flat over the window: engineering is the largest external field and declines slowly, the social532sciences, mathematics, medicine, psychology and decision sciences each hold a few per cent of references533with no visible change of direction in the post period, and medicine is the only external field whose share534rises slightly at the end of the window. On the v1 evidence the field-level version of H4 is not supported:535the boundary-crossing share of computer-science references toward other OpenAlex fields does not rise536after 2022, and the slow decline of the engineering share continues a trend visible in the baseline.537538This is a weaker statement than the one H4 makes, and the difference should be kept in view. The539hypothesis concerns boundaries \emph{within} computer science (systems toward AI, security toward AI,540human--computer interaction toward AI), and a field whose sub-areas converge on a common set of methods541may well cite less outside the field, not more, as its internal frontier absorbs the attention that used to542go to mathematics or engineering. The flat external shares are therefore compatible with H4 and with its543negation, and only the category flow matrices can decide between them. What the field-level curves do544establish is a boundary condition for the interdisciplinarity literature: the diversity indices of545Section~\ref{sec:m-diversity}, whether Rao--Stirling or Leinster--Cobbold, will be computed over a reference546distribution whose external component is small and stable, so that any change they detect will come from547the internal component. \citet{porter2009interdisciplinarity} found, for six fields over three decades, that548interdisciplinarity measured on references rose slowly and mostly through neighbouring fields; the549computer-science curves are consistent with that pattern and do not show the acceleration that the550foundation-model narrative would predict.551552\subsection{The age of cited work}553\label{sec:net-age}554555The age of the works a field cites is the simplest measure of how fast its knowledge turns over, and the556literature disagrees on its direction. \citet{evans2008narrowing} reported that online availability narrowed557citation toward fewer and more recent works; \citet{verstak2014giants}, in a preprint based on Google Scholar,558reported the opposite, a growing share of citations to older articles; \citet{parolo2015attention} measured559an accelerating decay of attention to individual papers as the volume of publication grew; and560\citet{chu2021slowed} argued that in very large fields the growth of publication itself ossifies the canon,561because new work cannot be read widely enough to displace it. Computer science is the field in which the562turnover is expected to be fastest, and \citet{frank2019citationgraphs} found that the AI citation graph had563become more self-referential and more recent-leaning over the 2010s.564565Figure~\ref{fig:cited_age} and Table~\ref{tab:cited_age} give the distribution of the age of cited works, the566citing year minus the cited work's publication year, for the resolved references of eligible works. The567cited-age file is the one graph table available at the time of writing, and it is a v1 file; the table will568be regenerated from the v2 file by the same script and its values are \pending{v2 graph}. On the v1569distribution, the mode of citation age is two years in every citing year, the mean falls monotonically from5702018 to 2025, the median falls from six to five years, the share of references to works at most five years571old rises by more than ten points over the window, and the share to works more than ten years old falls by572about the same amount. The shift is steady and does not accelerate at the 2022 boundary; the post-period573curves in the figure continue the movement of the baseline curves. A small share of references point to574works dated after the citing work, which arises from preprints cited before their published version carries575a later date and from year-only dates; this share falls over the window as the corpus's own dates become576first-appearance dates, and is excluded from the age statistics.577578\begin{figure}[htbp]579\centering580\includegraphics[width=0.95\textwidth]{fig_cited_age.pdf}581\caption{Distribution of the age of cited works (citing year minus cited year, 0 to 30 years) for five582citing years. Generated from the corpus v1 file \texttt{results/graph/cited\_age\_yearly.csv}; to be583regenerated for v2.}584\label{fig:cited_age}585\end{figure}586587The evidence therefore sides with \citet{evans2008narrowing} and \citet{parolo2015attention} rather than588with \citet{verstak2014giants} for this field and this window, with one reservation that the reference589coverage of OpenAlex imposes. If the probability that a reference string resolves to an OpenAlex record is590higher for recent, DOI-bearing works than for older ones, as \citet{culbert2025openalexcoverage} report in591their comparison with Web of Science and Scopus, then the resolved references are biased toward youth, and a592constant true age distribution would appear to become younger as the resolvable share rises. The reference593coverage table of the methodology (declared, internal and external references by year) is the control for594this and is part of the pending v2 graph; the age shift is reported here as observed, not as corrected.595596\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_cited_age}\endgroup597598\subsection{Knowledge flows between categories}599\label{sec:net-flows-categories}600601The flow matrices $F_t$ between the categories of the ontology, the cross-area shares $X_{\alpha,t}$ of602equation~\eqref{eq:cross-area} and the yearly modularities $Q_{\mathrm{cat}}$ and $Q_{\mathrm{area}}$ of603equation~\eqref{eq:modularity} are the statistics on which H4 turns and the ones that would show whether604systems, security and human--computer interaction cite the AI categories more after 2022 than before. They605require the primary category of every work and are produced by606\texttt{knowledge\_graph/02\_category\_flows.py} once the classification of Part~IX is complete. The result607files \texttt{category\_flows\_yearly.csv}, \texttt{cross\_area\_share\_yearly.csv} and608\texttt{modularity\_yearly.csv} do not exist at the time of writing, and this subsection is609\pending{category flows after classification}. When it is filled, it should report, for each citing area, the610cross-area share by year with the composition-adjusted variant of Section~\ref{sec:m-networks}, the two611modularities with the self-share, and a comparison of the baseline and post means with the caveat that the612post-period citing years have shorter reference lists in the incomplete 2026 row.613614\section{The boundary of the database}615\label{sec:net-boundaries}616617\subsection{What DBLP sees that the corpus does not}618619The corpus is the union of several sources resolved to OpenAlex records (Section~\ref{sec:data-linkage}),620and a DBLP record without an OpenAlex counterpart cannot enter it, because the citation, affiliation and621topic data on which every indicator of this part depends are OpenAlex's. Table~\ref{tab:dblp_only} counts622these records by DBLP type and year. They are a small fraction of DBLP's annual output, and their623composition is specific: journal articles with a DOI that OpenAlex has not indexed or has indexed under a624different identifier, conference papers mostly without a DOI, which are the hardest to link by title, and625doctoral theses, which DBLP indexes from a few national repositories and OpenAlex largely does not. The626``data'' type, DBLP's record of datasets and software, grows across the window and is almost entirely627unmatched, which is a reminder that the research outputs of computer science that are not papers are628outside the corpus altogether. For 2026 the conference share of the unmatched records rises sharply, which629is the DBLP-side manifestation of the right truncation discussed in Section~\ref{sec:data-dates}: DBLP630indexes a proceedings volume as a whole when it appears, OpenAlex matches it paper by paper over the631following months, and the gap is largest in the most recent year. The missing records bias the indicators632of this part toward the parts of computer science that publish with DOIs in journals and large conference633series, that is, away from theses, workshop papers and national venues; the direction of the bias is known634and its magnitude is bounded by the table.635636\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_dblp_only}\endgroup637638\subsection{Why the creation date does not measure indexing lag}639640The research plan proposed to estimate the indexing delay of OpenAlex from the \texttt{created\_date} of641each record and to correct the recent months of the publication series for it. Part~III642(Section~\ref{sec:data-dates}) records why the proposal was abandoned; Table~\ref{tab:indexing_lag} gives643the evidence in annual form. For every publication year up to 2024, the median lag between publication and644record creation is of the order of years, it is larger for January than for June publications by almost645exactly five months, and more than nine tenths of the year's records were ``created'' more than 180 days646after publication. A genuine indexing delay cannot have that shape: it would be measured in weeks or647months, would not depend on the month of publication within the year, and would not place nearly all648records beyond the 180-day mark. The shape is that of a single creation date for the bulk of the database,649with the lag equal to the time between each work's publication and that date, which places the date in the650second half of 2025. For works published in 2025 and 2026 the field behaves differently: a large share of651records is created within 90 days of publication, and the median lag collapses to days by mid-2026. The652field therefore measures the delay only for records created after the re-ingestion, and only for them653would a lag profile be meaningful; a profile estimated from the whole table, or from the years that the654structural-change analysis needs for its pre-trend diagnostics, would be an artefact of database655maintenance. This is the reason the structural-change analysis truncates the series rather than correcting656it (Section~\ref{sec:m-truncation}), and it is the reason the only honest estimator of indexing lag is the657comparison of two snapshots of the same database, which the released raw snapshots make possible for a658future study.659660\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_indexing_lag}\endgroup661662\section{Hypotheses H4--H6 at this stage}663\label{sec:net-hypotheses}664665The protocol states its hypotheses with a direction so that null and opposite results are reported as666such. On the evidence of this part, the verdicts are the following, each limited to the component of the667hypothesis that the available tables test.668669H4 (convergence) is not testable in its stated form, which concerns citation flows between areas of the670ontology and the modularity of the area network; those statistics await the classification. Its field-level671counterpart, the share of computer-science references that cross into other OpenAlex fields, is flat over the672window on the v1 graph (Section~\ref{sec:net-flows-fields}), which neither supports nor contradicts the673within-field convergence the hypothesis describes.674675H5 (concentration) has two components. The citation-inequality component is stated for AI categories and is676pending; its aggregate counterpart gives a Gini of three-year citations that falls through the baseline and677rises for the one complete post-period cohort, a movement dominated by the share of uncited works and by678right truncation, and therefore not interpretable as a change in concentration. The venue-concentration679component predicted a stable or lower index once preprints are treated separately; the index with arXiv680included rises, for the mechanical reason the protocol anticipated, and the index without the preprint type681is pending. The non-arXiv venue landscape widens.682683H6 (geography and collaboration) has three components. The international co-authorship share does not684rise, as predicted, and in fact declines slightly, with a composition explanation that the country shares685support. The China share rises in the aggregate under both counting conventions, as predicted, but as the686continuation of a baseline trend, and the category-specific version is pending. The industry share does687\emph{not} rise in the aggregate: it peaks in 2021 and declines in every post-period year, which is the688opposite of the predicted direction, with the category-specific version pending and with the frontier-level689measures of the literature it was drawn from measuring a different object.690691What the part adds beyond the hypotheses is a set of structural observations that were not predicted and692that the pending analyses will have to accommodate: the fall in absolute joint output between China and the693United States during a period in which both grew; the stability of the institutional hierarchy; the rise of694generalist repositories among the largest sources of computer-science records; the steady shift of695references toward younger work without acceleration at the boundary; and the record-level artefacts in the696most-cited lists, which make any ranking of influential works conditional on an audit that this part has697specified but not performed.698699