spb/wp44_uqo

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/*.csv (corpus v3 graph, 2026-11-03 18:44;4% tables tab_field_flows, tab_reference_coverage, tab_cited_age regenerated from them by tables/make_tables.py, Agent L/M).56\section{Scope and reading rules}7\label{sec:net-scope}89This part reports what the eligible corpus shows about the people, organisations, countries and venues that10produce computer-science research, about the distribution of attention over the works they produce, and about11the sources on which that research draws. It is the empirical counterpart of research questions RQ4 and RQ612and of the networks section of the methodology (Section~\ref{sec:m-networks}), and it tests the parts of13hypotheses H4, H5 and H6 that the current result files make testable. The citation-flow statistics between14taxonomy categories, which carry the main weight of H4, depend on the classification of Part~IX and are not15yet available; Section~\ref{sec:net-flows-categories} is a placeholder for them. The reader should16therefore expect a part that is complete on collaboration, geography, institutions, venues and aggregate17citation structure, and provisional on knowledge flows.1819Three reading rules apply throughout. First, every indicator is computed on the eligible corpus defined in20Part~III (Section~\ref{sec:data-eligibility}), so that ``computer science'' means the union of DBLP-indexed,21OpenAlex-primary-field and arXiv \texttt{cs} works after the exclusions of the PRISMA flow, and the indicators22inherit the boundary decisions and the affiliation completeness of that corpus. Second, the two periods of the23protocol are unequal in length and in completeness: the baseline runs from January 2018 to the end of24November 2022, the post period from December 2022 to the snapshot of October 2026 (the API increment of25Part~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 in26Section~\ref{sec:data-dates}. Tables by year therefore carry 2026 as an incomplete row, and the fixed-window27citation statistics of Section~\ref{sec:net-citations} are complete only up to the publication years flagged in28Table~\ref{tab:citation_windows}. Third, the comparison of periods is descriptive. The protocol states the29hypotheses with a direction so that null and opposite results can be reported as such, and several of the30results below are of that kind; none of them is evidence of an effect of any single event, and the language of31this part is deliberately that of association and composition.3233The part is organised from the smallest unit of production outward. Section~\ref{sec:net-teams} describes34authorship and team structure; Section~\ref{sec:net-international} the international co-authorship network;35Section~\ref{sec:net-geography} the geography of output; Section~\ref{sec:net-institutions} institutions and36sectors, including the industry share that H6 concerns; Section~\ref{sec:net-venues} publication channels and37venue concentration; Section~\ref{sec:net-citations} the distribution of citations and its inequality;38Section~\ref{sec:net-flows} the inflows of knowledge from other fields and the age of the works cited;39Section~\ref{sec:net-boundaries} the boundary of the database itself, through the DBLP-only records and the40\texttt{created\_date} diagnostic; and Section~\ref{sec:net-hypotheses} collects the verdicts on H4--H6.4142\section{Authorship and team structure}43\label{sec:net-teams}4445The long-run growth of team size in science is one of the most replicated findings of scientometrics:46\citet{wuchty2007teams} documented the shift from solo to team production across fields over five decades,47\citet{lariviere2015teamsize} extended the series back to 1900 and showed that the citation advantage of teams48has grown with it, and \citet{milojevic2014teams} proposed a generative account in which a core of small,49``Poisson-like'' teams coexists with an expanding tail of large ones. Computer science has long been a field of50small teams by the standards of the laboratory sciences, which is why the question for this corpus is not51whether teams grow but whether the rate of growth or the shape of the distribution changes across the 202252boundary. The hypothesis set of the protocol does not take a position on team size, and the evidence is53reported for its own sake and as a control for the collaboration indicators that follow.5455Table~\ref{tab:collaboration} gives the annual series, and Figure~\ref{fig:collaboration} plots the mean and the56tail shares. The mean number of authors per eligible work rises from57\VolumeYearlyTwoZeroOneEightMeanAuthors{} in 2018 to \VolumeYearlyTwoZeroTwoTwoMeanAuthors{} in 2022 and58\VolumeYearlyTwoZeroTwoFiveMeanAuthors{} in 2025, a monotone increase at a pace that does not visibly change at59the boundary; the median stays at three authors in every year, so the growth of the mean is a growth of the60upper tail. The tail shares in the table make the same point: the share of works with five or more authors61rises steadily, and the share with ten or more, although small, roughly triples over the window. The62single-author share falls through 2022 and then rises again, sharply in 2025 and 2026. That reversal is not a change in63research practice. The column of works without any resolved country shows the same U-shape, and the64single-author and unaffiliated shares move together because the records that enter the corpus fastest after65publication (preprints, repository deposits, records not yet enriched with affiliations) are also those whose66authorship metadata is least complete; as those records are enriched and matched to their published versions67in later snapshots, both shares fall. The 2025 and 2026 rows of Table~\ref{tab:collaboration} must therefore68be read as a snapshot of the indexing process as much as of authorship, and the pre-2024 trend is the only69part of the series on which a substantive statement rests.7071\begin{figure}[htbp]72\centering73\includegraphics[width=0.95\textwidth]{fig_collaboration.pdf}74\caption{Team size, international co-authorship and industry participation by year. Mean authors per work and75tail shares from \texttt{team\_size\_yearly.csv}; the international share is the ICS of Part~IV (works with76two or more countries among works with at least one); the company share is over works with at least one77typed affiliation (\texttt{industry\_share\_yearly.csv}). 2026 is incomplete.}78\label{fig:collaboration}79\end{figure}8081\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_collaboration}\endgroup8283The multi-institution share, the fraction of works whose authors list more than one distinct institution,84follows the mean team size through 2022 and then declines, with the same affiliation-completeness85explanation as the single-author reversal: an unaffiliated record cannot be multi-institutional. Here the86substantive literature gives a reason to expect genuine growth. \citet{jones2008multiuniversity} showed that87multi-university collaboration had become the fastest-growing form of team production in the United States,88with a citation premium concentrated in the top-tier institutions, and \citet{adams2013fourthage} argued89that a ``fourth age'' of research organised around international networks of elite institutions was90displacing the national systems of the previous one. The corpus is consistent with continued growth of91multi-institution work up to the point where the affiliation data become unreliable and is silent beyond it.9293Two cautions apply to all of these shares, and they are not specific to this corpus. The first is that94OpenAlex author counts are taken from the authorship lists of the surviving record after deduplication95(Section~\ref{sec:m-dedup}); where a preprint and its published version differ in author list, the published96version wins, which is the appropriate choice but one that makes the count depend on the linkage. The second97is that very large author lists in computer science come disproportionately from a few genres, namely98consortium reports, shared-task overviews and large model ``technical reports'', so that the ten-plus share99measures the prevalence of those genres as much as the size of ordinary research teams. The disruption100literature attaches a substantive interpretation to team size, with \citet{wu2019disruption} reporting that101small teams produce more disruptive work and large teams more developmental work; that interpretation is102not tested here, because the disruption index requires a citation graph with a long post-publication horizon103that the post period does not yet provide.104105\section{International co-authorship}106\label{sec:net-international}107108International collaboration has grown in every field and every country for which long series exist109\citep{wagner2015cooperation, wagner2017collaboration}, and the growth has been described as the emergence110of a self-organising global network with a core group of countries that is stable over time111\citep{leydesdorff2008core}. The protocol's H6 predicts, against this background, that the international112co-authorship share of computer science does \emph{not} rise in the post period. The prediction was motivated113by two considerations stated in the protocol discussion: the geopolitical restriction of some114bilateral channels after 2020, and the shift of a growing share of the field's output into115preprint channels and into countries whose output is predominantly domestic.116117The international collaboration share (ICS, Section~\ref{sec:m-bibliometrics}) is computed among works with118at least one resolved country, so that the affiliation-completeness problem of the previous section does not119enter the denominator. Its yearly values are in the last column of Table~\ref{tab:collaboration} and are120macro-reported here for the end points: \InternationalCollabYearlyTwoZeroOneEightShareIntl{} in 2018,121\InternationalCollabYearlyTwoZeroTwoZeroShareIntl{} in 2020, \InternationalCollabYearlyTwoZeroTwoTwoShareIntl{}122in 2022, \InternationalCollabYearlyTwoZeroTwoFourShareIntl{} in 2024 and123\InternationalCollabYearlyTwoZeroTwoFiveShareIntl{} in 2025. The series is flat to slightly declining: it124peaks in 2020, is lower in every subsequent year, and the post-period values are below every baseline value.125The null part of H6 is therefore supported in the direction stated, and the result is in fact stronger than126the hypothesis, which only predicted the absence of a rise. Two qualifications prevent a stronger reading.127The denominator grows faster than the numerator over the window128(\InternationalCollabYearlyTwoZeroOneEightN{} works with a country in 2018 against129\InternationalCollabYearlyTwoZeroTwoFiveN{} in 2025), and the composition of that growth, examined in the next130section, is dominated by countries with low international shares; a constant propensity to collaborate within131every country would produce exactly this aggregate decline. And the share is a share of works, not of132authors or of citations, so that the increasing size of international teams noted by133\citet{wagner2017collaboration} would not register in it.134135The 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 works136in a period. The threshold is a reporting choice (Section~\ref{sec:m-bibliometrics}); it keeps the network to137the pairs whose weight is robust to small linkage errors, at the cost of excluding the long tail of weak ties138through which, in the account of \citet{leydesdorff2008core}, peripheral countries enter the core. On this139restricted network, the number of edges and the number of countries both increase from the baseline to the140post period even though the post period is about ten months shorter, so the network densifies at the141threshold. The ordering of countries by strength, the sum of a country's edge weights, changes at the top:142the United States has the largest strength in the baseline and China in the post period, with the United143Kingdom third in both. The twenty strongest pairs (Table~\ref{tab:country_pairs}) show where the change comes144from. The China--United States pair is the heaviest edge in both periods, but its weight is lower in the post145period than in the baseline in absolute terms, while the pairs of China with Hong Kong, Singapore, the United146Kingdom and Australia rise in weight, and Hong Kong and Singapore rise in rank; the China--Hong Kong pair147moves from fourth to second.148The share of the China--United States edge in the total weight of the network falls accordingly149(Table~\ref{tab:country_network}). A decline in the absolute volume of joint work between the two largest150producers, in a period in which the output of both grew, is the most distinctive structural feature of the151collaboration data, and it is consistent with the bilateral-restriction channel that motivated H6; it is152not, on its own, evidence about the cause, and the reader should note that Hong Kong and Macau carry their153own country codes in OpenAlex, so that part of the apparent reorientation of China's collaboration is a154reorientation toward its own special administrative regions.155156Most of the rest of the pair table is continuity. The United Kingdom--United States, Germany--United157States and Germany--United Kingdom pairs keep approximately their weights; the India--United States pair158rises; the Canada--China and Canada--United States pairs fall slightly; and the France--United States and159Australia--United States pairs fall more and drop in rank, two movements that the table records and this160part does not explain. The picture is that of a core group whose composition is stable, as161\citet{leydesdorff2008core} and \citet{glanzel2001national} found for science as a whole, with one edge162weakening and a cluster of East-Asian edges strengthening. Degree-based statistics of the network163(density, clustering, assortativity) are not reported, because at a fixed weight threshold they measure164the growth of the corpus as much as the structure of collaboration; the strength ordering and the pair165weights, which are counts, are the statistics that survive that objection.166167\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_country_network}\endgroup168\input{tables/tab_country_pairs}169170\section{The geography of production}171\label{sec:net-geography}172173The country-level composition of output is the part of this study where the counting convention matters174most, and the methodology (Section~\ref{sec:m-bibliometrics}) reports both. Under full counting a work with175authors in three countries is counted once for each; under fractional counting it is divided among them.176The two conventions give different levels, and the difference is itself informative, because a country whose177full-count share is much larger than its fractional share is one whose output is predominantly178collaborative \citep{gauffriau2008counting, waltman2015counting}. Table~\ref{tab:countries} gives the179fractional counts of the fifteen largest countries by year, Table~\ref{tab:country_shares} the corresponding180shares, Table~\ref{tab:country_concentration} the concentration of the distribution and the full-count shares181of the two largest producers, and Figure~\ref{fig:country_shares} the shares of the eight largest.182183\begin{figure}[htbp]184\centering185\includegraphics[width=0.95\textwidth]{fig_country_shares.pdf}186\caption{Country shares of eligible output under fractional counting, eight largest countries by cumulative187output. Each work is divided equally among its distinct author countries; works without a resolved country188are excluded. Source: \texttt{results/bibliometrics/countries\_yearly.csv}. 2026 is incomplete.}189\label{fig:country_shares}190\end{figure}191192The dominant movement is the rise of China's share, which is already the largest in 2018 and grows in every193complete year of the window, under both counting conventions. The second is the decline of the United194States' share, which is monotone through 2025 under both conventions and recovers only in the incomplete1952026 row, where the fast channels in which American output is over-represented (preprint servers) weigh more196than they will once the year is fully indexed. The third is the growth of India and, more sharply in197relative terms, Indonesia, which enters the top five by the end of the window; the fourth is the slow198relative decline of the large European producers, Japan and Korea, whose absolute output is flat or rising199(Table~\ref{tab:countries}) while the total grows. The Russian series falls after 2021 and does not200recover. These movements are gradual and are visible in the baseline as well as in the post period;201nothing in the country shares changes direction at the 2022 boundary, and the growth of China's share is202if anything slower in 2024 and 2025 than in 2021 and 2022.203204The China part of H6 asks whether the share of works with China-affiliated authors rises in the post period205\emph{in the AI categories}. The aggregate rise is established by Table~\ref{tab:country_concentration},206whose column of works with a China-affiliated author is the quantity the hypothesis names. The207category-specific version uses the primary category of Part~IX: Table~\ref{tab:net_category_actors} gives,208for each of the forty categories, the share of works with a China-affiliated author in the baseline and in209the post period, Table~\ref{tab:net_ai_vs_rest} pools the nine categories of the AI/ML area against the210thirty-one others, and Table~\ref{tab:net_ai_vs_rest_yearly} gives the two pooled series by year. Three211things must be said before reading them. The denominator of these shares is every work of the category,212including works without affiliation data, so the level is below that of Table~\ref{tab:country_concentration}213and is depressed wherever affiliation coverage is low, which is the case for the most recent cohorts and for214preprint-heavy categories; the within-category comparison across periods is affected to the extent that215coverage changed. The grouping by primary category assigns a work to one category only, so a vision paper216that uses a language model counts under computer vision, not under large language models. And the AI/ML217area of the ontology is wider than the four categories that define the post period, since it also contains218reinforcement learning, machine-learning theory, deep-learning architectures, agents and AI safety.219220With these qualifications, the China share rises from the baseline to the post period in the AI/ML area, as221H6 predicts, and it rises in the pooled other areas as well, by a larger margin; the note of222Table~\ref{tab:net_category_actors} counts the categories in which the share rises, and the rise is close to223universal outside the AI/ML area. Within the AI/ML area the rise is carried by the older categories,224reinforcement learning, deep-learning architectures and agents, while the categories that define the post225period behave differently: the share is nearly flat for large language models, falls for foundation models and226generative AI, and is highest of all forty categories, in both periods, for multimodal AI. The United States227share falls in both groups and in most categories; agents and large language models are the AI/ML228categories in which it rises. The yearly series of Table~\ref{tab:net_ai_vs_rest_yearly} show the pooled229shares of the two groups moving together: both rise through 2023 and fall in 2024 and 2025, and the gap230between them, roughly constant through 2023, closes in 2024 and 2025. The fall after 2023 coincides with the lower231affiliation coverage of recent cohorts (Section~\ref{sec:net-teams}) and cannot be read as a reversal; what232it does establish is that the AI/ML area is not where the China share grows fastest. The verdict on this233component of H6 is therefore a supported direction with an unsupported specificity: the share rises in AI234categories, but less than elsewhere, and the rise is the continuation of a trend that predates the window and235is documented in every recent comparison of national output \citep{bornmann2021growth}.236237Concentration across countries, measured by the Herfindahl--Hirschman index of fractional shares and by the238shares of the five and ten largest countries, rises through 2025 (Table~\ref{tab:country_concentration}).239The index is dominated by the largest share, so the rise is mostly China's rise; the top-ten share moves240less than the top-five share, which means that the countries ranked six to ten lose share to those ranked241one to five rather than to the tail. The number of countries with any output is stable. The widely242discussed concern that the geography of AI research is narrowing \citep{klinger2020narrowing,243ahmed2020dedemocratization} is a concern about institutions and compute rather than about countries, and the244country-level concentration measured here speaks to it only indirectly; the institutional evidence is in the245next section.246247The ratio of a country's full count to its fractional count, in the last two columns of248Table~\ref{tab:country_concentration}, exceeds one by the extent to which its works are co-authored with249other countries, and it is informative about collaboration intensity. China's ratio is lower than the United250States' in every year, which is the signature of a more domestic output: a larger fraction of251Chinese-affiliated works has only Chinese affiliations. Since China's share grows and the252United States' falls, the aggregate international share of Section~\ref{sec:net-international} is pulled253down by composition even if no country's propensity to collaborate changes. This is the mechanical254channel behind the null result on international collaboration, and it is the reason that result is255reported with the composition caveat rather than as a change in behaviour.256257\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_countries}\endgroup258\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_country_shares}\endgroup259\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_country_concentration}\endgroup260\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_net_category_actors}\endgroup261\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_ai_vs_rest}\endgroup262\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_ai_vs_rest_yearly}\endgroup263264\section{Institutions and sectors}265\label{sec:net-institutions}266267\subsection{The sectoral mix of affiliations}268269OpenAlex types every institution as education, facility, company, government, healthcare, nonprofit,270funder, archive or other. Table~\ref{tab:institution_types} gives the distribution of typed affiliations over271these classes by year, and Table~\ref{tab:industry} the share of works with at least one company affiliation,272which is the statistic named by H6. The hypothesis predicts that the industry share rises in the post period273in AI categories. The prediction follows a line of work that has documented the growing weight of industry in274machine-learning research: \citet{frank2019citationgraphs} traced the shift of the AI citation graph toward275industry-authored and computer-science-internal sources, \citet{ahmed2023industry} reported that industry's276share of the largest models, of the most cited papers and of the field's PhD graduates had risen sharply in277the decade to 2022, and \citet{klinger2020narrowing} argued, in a preprint, that the thematic diversity of AI278research had narrowed as the private sector's share rose.279280The aggregate corpus does not show a rising industry share. The company share of works with a typed281affiliation is \IndustryShareYearlyTwoZeroOneEightShareCompany{} in 2018, rises to a maximum of282\IndustryShareYearlyTwoZeroTwoOneShareCompany{} in 2021, and then falls in every subsequent year to283\IndustryShareYearlyTwoZeroTwoFiveShareCompany{} in 2025, which is below the 2018 value; the incomplete2842026 row is at \IndustryShareYearlyTwoZeroTwoSixShareCompany{}. The absolute number of works with a company285affiliation keeps growing (\IndustryShareYearlyTwoZeroOneEightNCompany{} in 2018 against286\IndustryShareYearlyTwoZeroTwoFiveNCompany{} in 2025), so the falling share is a matter of the denominator287growing faster: the growth of the post-period corpus comes disproportionately from education-sector output,288and within that from the countries of Section~\ref{sec:net-geography} whose output is almost entirely289academic. Table~\ref{tab:institution_types} shows the same thing from the other side, with the education290share of affiliations rising through the window and the facility, government and company shares all giving291way. The aggregate part of H6 is therefore not supported; the sign is opposite to the one predicted. Whether292the category-specific version holds, that is, whether the company share rises within the AI categories while293falling in the aggregate, is exactly the kind of composition question that the aggregate cannot settle, and294Tables~\ref{tab:net_category_actors}, \ref{tab:net_ai_vs_rest} and~\ref{tab:net_ai_vs_rest_yearly} settle it295in the negative. The company share of the AI/ML area is higher than that of the other areas in every year,296which is the familiar result that industry is more present in machine learning than in the rest of computer297science; but it peaks in 2021 and falls in every subsequent complete year, so that the baseline-to-post decline of the298AI/ML area is larger than that of the other areas, not smaller. The note of299Table~\ref{tab:net_category_actors} counts the categories whose company share rises: one of the nine AI/ML300categories (agents), against a sizeable minority of the others, among them cloud computing, information301retrieval, distributed computing, database systems, operating systems and quantum computing. The AI/ML302categories with the highest baseline company shares, multimodal AI, reinforcement learning, foundation303models and large language models, all lose share in the post period, and generative AI loses more than304half of its share. The denominator caveat of the previous paragraph applies with more force here than for the305China share, because the AI/ML area has the highest share of arXiv-linked works306(Table~\ref{tab:net_ai_vs_rest}) and preprints are the records least often enriched with affiliations; part of307the measured decline is therefore coverage. Nothing in the category tables, however, suggests the opposite308sign for the AI categories, and the frontier-share results of \citet{ahmed2023industry} remain the only309sense in which an industry share has risen.310311The result is less at odds with the cited literature than it seems, for three reasons that matter for its312interpretation. \citet{ahmed2023industry} measure industry's presence at the frontier---the largest models,313the most cited papers, the leading conferences---and not its share of all output; a sector can dominate the314frontier of a field while its share of the field's total publications falls, and the two facts are compatible315with a frontier that is increasingly expensive to reach \citep{ahmed2020dedemocratization}. Second, the316OpenAlex institution type is assigned to the institution, not to the author's role, so a work by a317corporate research laboratory published with an academic co-author counts as both, and the share reported318here is the share of works with \emph{any} company affiliation, which is the most inclusive definition.319Third, the affiliation completeness problem of Section~\ref{sec:net-teams} affects the typed denominator:320records without affiliation data are excluded, and if industry-authored preprints are less often enriched321with affiliations than journal articles, the company share of recent years is understated. None of these322reasons reverses the aggregate finding, but together they confine it to what it measures.323324\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_industry}\endgroup325\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_institution_types}\endgroup326327\subsection{Institutional concentration and stability}328329The institution tables (Tables~\ref{tab:institution_concentration} and~\ref{tab:top_institutions}) list330institutions with at least two hundred works in a period, identified by their OpenAlex identifiers only; the331result files do not carry institution names, and this part refrains from resolving the identifiers by hand so332that every statement remains reproducible from the released artefacts. The number of institutions above the333threshold rises from the baseline to the post period, as does the number of works they account for, in both334counting conventions. The ratio of full to fractional counts among the largest institutions is close to two,335meaning that the average work of a large institution carries about one other institution, which is the336multi-institution pattern of Section~\ref{sec:net-teams} seen from the institution's side.337338Concentration among the listed institutions is low and stable: the ten largest account for a few per cent of339the listed fractional output and the hundred largest for less than a quarter, with both shares slightly340higher in the post period. This is a different picture from the one that the concern over the341``de-democratisation'' of AI research conveys \citep{ahmed2020dedemocratization}, and the difference is again342one of object: the distribution of \emph{all} computer-science output over institutions is wide, whereas the343distribution of the frontier of one sub-area may be narrow, and only the latter has been claimed to be344narrowing. The rank stability of institutions across periods is high: of the institutions listed in the345baseline, the great majority are also listed in the post period, and the Spearman correlation of their346fractional counts across the two periods, given in the note to Table~\ref{tab:institution_concentration}, is347close to nine tenths. Among the institutions listed in both periods, the twenty-five largest of the post period348(Table~\ref{tab:top_institutions}) have post-to-baseline ratios that cluster around or somewhat above the349ratio of the two periods' listed totals, with a few institutions growing considerably faster and two of the350largest full-count producers growing slower than the corpus. The institutional hierarchy of computer science, in other words, was not reshuffled in the351post period; it grew in place.352353\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_institution_concentration}\endgroup354\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_top_institutions}\endgroup355356\section{Publication channels and venue concentration}357\label{sec:net-venues}358359The venue is the unit at which the publishing system intersects the research system, and the two have been360changing in opposite directions in computer science for two decades: the publishing side has consolidated361into a small number of commercial and society publishers \citep{lariviere2015oligopoly}, while the research362side has moved a growing share of its first dissemination to arXiv363\citep{sutton2017arxivcs, lin2020arxivcs, lariviere2014arxiv}. The OpenAlex notion of source, on which the364tables of this section are built, follows the venue (a journal, a conference series, a book series, a365repository, an ebook platform) rather than the publisher, so what is measured here is concentration over366venues, and arXiv counts as one venue. The protocol's H5 anticipated this when it predicted that venue367concentration would be ``stable or lower because of preprint growth'' once the preprint source is treated368separately; the methodology (Section~\ref{sec:m-bibliometrics}) notes that the index with arXiv included369rises mechanically with preprint growth.370371Table~\ref{tab:venue_hhi} and Figure~\ref{fig:venue_concentration} give the yearly number of distinct sources,372the Herfindahl--Hirschman index over sources and the share of the largest source. The number of distinct373sources rises every complete year, from \VenueHhiYearlyTwoZeroOneEightNSources{} in 2018 to374\VenueHhiYearlyTwoZeroTwoFiveNSources{} in 2025, so the venue landscape is widening in the sense of variety.375The index, however, rises as well: from \VenueHhiYearlyTwoZeroOneEightHhi{} in 2018 to376\VenueHhiYearlyTwoZeroTwoFiveHhi{} in 2025 and \VenueHhiYearlyTwoZeroTwoSixHhi{} in the incomplete 2026377row, and the share of the largest source, which is arXiv in every year, goes from378\VenueHhiYearlyTwoZeroOneEightTopOneShare{} to \VenueHhiYearlyTwoZeroTwoFiveTopOneShare{} and then to379\VenueHhiYearlyTwoZeroTwoSixTopOneShare{} in 2026. The index is small in absolute terms (its upper bound is380one, reached when a single venue carries all works), and the squared share of arXiv accounts for most of it381in the later years; the 2026 value is an artefact of right truncation, since preprints are indexed within382days and journal and conference records months later (Section~\ref{sec:data-dates}), and will fall as the383year completes. The concentration result is therefore the one the protocol expected in mechanism and the384opposite of the one it expected in sign: concentration over venues, with arXiv counted as a venue, rises385because of preprint growth, and the version of the index without the preprint type, which H5 names, is386\pending{venue HHI excluding preprints}. The qualitative conclusion that does not depend on it is that the387rest of the venue landscape is not concentrating: the number of venues grows, and the second-ranked sources388in Table~\ref{tab:top_sources} hold shares that are an order of magnitude below arXiv's.389390\begin{figure}[htbp]391\centering392\includegraphics[width=0.95\textwidth]{fig_venue_concentration.pdf}393\caption{Number of distinct sources per year (left) and venue concentration (right): Herfindahl--Hirschman394index over sources, scaled by $10^4$, and share of the largest source, which is arXiv in every year.395Source: \texttt{results/bibliometrics/venue\_hhi\_yearly.csv}. 2026 is incomplete and inflated by the396faster indexing of preprints.}397\label{fig:venue_concentration}398\end{figure}399400Tables~\ref{tab:source_types} and~\ref{tab:top_sources} describe the channels themselves. By source type,401journals carry about half of the listed works in both periods, conferences between a fifth and a quarter,402and repositories rise from about an eighth to about a fifth between the baseline and the post period, at403the expense of conferences, book series and ebook platforms. The twenty largest sources make the composition concrete. arXiv404is first in both periods and more than doubles its count; Lecture Notes in Computer Science is second in both;405SSRN, which is not a computer-science venue but hosts a growing number of works that OpenAlex classifies in the406field, moves from the lower part of the baseline list to third; Research Square and NeurIPS enter the407post-period list and the AAAI conference proceedings rise within it; the large open-access408journals (IEEE Access, Sensors, Remote Sensing) remain in the list but with lower counts in the post period409than in the baseline, a decline whose cause (editorial policy, reclassification by OpenAlex, or the shorter410period) the corpus does not identify. The411appearance of generalist repositories (SSRN, Research Square, OSF) among the largest computer-science412sources is a boundary effect of the OpenAlex topic classification rather than a change in where computer413scientists publish, and it is one of the reasons the strict-core sensitivity set of Part~III exists.414415\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_venue_hhi}\endgroup416\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_source_types}\endgroup417\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_top_sources}\endgroup418419\section{The distribution of citations}420\label{sec:net-citations}421422\subsection{Levels, zeros and inequality within fixed windows}423424Citation distributions are heavy-tailed in every field, and the degree of skewness is remarkably similar425across fields once counts are normalised by the field mean \citep{seglen1992skewness, radicchi2008universality,426albarran2011skewness}. The mechanisms proposed for the tail are cumulative advantage, the ``Matthew effect''427by which recognised work attracts recognition \citep{merton1968matthew, price1976cumulative}, and its428network formalisation as preferential attachment \citep{barabasi1999scaling}; the mechanism proposed for the429mass of the distribution is a combination of a work's intrinsic fitness and an ageing function430\citep{wang2013longterm}. What a cross-period comparison can measure is not these mechanisms but the shape431of the distribution at a fixed exposure, and the fixed windows of Section~\ref{sec:m-citations} are the device432that makes the shape comparable: $c^{(36)}$ counts the citations received in the publication year and the two433following calendar years, and is complete for publication years up to 2023.434435Table~\ref{tab:citation_windows} and Figure~\ref{fig:citation_inequality} give the yearly statistics. The mean436of $c^{(36)}$ rises from \CitationWindowsYearlyTwoZeroOneEightMeanCThreeSix{} for works published in 2018 to437\CitationWindowsYearlyTwoZeroTwoTwoMeanCThreeSix{} for 2022 and438\CitationWindowsYearlyTwoZeroTwoThreeMeanCThreeSix{} for 2023, the last complete year; the median is one439citation in most years and two in 2022, so the mean is carried by the tail. The share of works uncited at440three years falls from \CitationWindowsYearlyTwoZeroOneEightShareUncitedThreeSix{} for 2018 to441\CitationWindowsYearlyTwoZeroTwoTwoShareUncitedThreeSix{} for 2022 and rises again to442\CitationWindowsYearlyTwoZeroTwoThreeShareUncitedThreeSix{} for 2023. Both movements are what a growing443citing population produces: each publication year is cited by the following two years' output, and that output444grows, so later cohorts receive more citations at equal exposure \citep{bornmann2015growth}. The reversal in4452023 is the first sign of right truncation in the window, since the third calendar year of the 2023 cohort446is 2025, for which the slower channels of indexing (and citation extraction) are not complete; it is447flagged in the table and is the reason the 2024 row, whose window is formally incomplete, is not used.448449The Gini coefficient of $c^{(36)}$ is the inequality statistic named, with a deviation in window length450recorded in Section~\ref{sec:m-bibliometrics}, by H5. It falls from451\CitationWindowsYearlyTwoZeroOneEightGiniCThreeSix{} for 2018 to452\CitationWindowsYearlyTwoZeroTwoTwoGiniCThreeSix{} for 2022, then rises to453\CitationWindowsYearlyTwoZeroTwoThreeGiniCThreeSix{} for 2023; the 12-month Gini follows the same path at a454slightly higher level, as expected from the larger share of zeros in the shorter window. Since the share of455uncited works moves with the Gini, and uncited works are the main contributor to inequality in a short window456(Section~\ref{sec:m-bibliometrics}), the fall through 2022 is to a large extent a fall in the share of zeros457rather than a change in the shape of the tail, and the 2023 uptick is the truncation effect just described.458H5 predicts that citation inequality is higher in the post period than in the baseline \emph{for AI459categories}. The aggregate series can test only the aggregate statement, and for the one post-period460publication year with a complete window (2023) the aggregate Gini is above the 2022 value and below every461baseline value before 2021, so the aggregate evidence is mixed and dominated by truncation. The category462version of the test, which is the one the hypothesis states, is in Table~\ref{tab:net_category_gini}, which463gives the Gini of $c^{(36)}$ by primary category for every publication year with a complete window, and in464Table~\ref{tab:net_gini_ai_vs_rest}, which pools the AI/ML area against the other areas as work-weighted means465of the category statistics. Two patterns are visible. Between the 2018 and 2022 cohorts the within-category Gini falls in466almost every category, as the aggregate does, and for the same reason, the falling share of uncited works;467the exceptions are algorithms and large language models.468For the 2023 cohort the pooled AI/ML Gini is above its baseline mean while the pooled Gini of the other469areas is below its own; the note of Table~\ref{tab:net_category_gini} counts the categories whose 2023 value470exceeds their baseline mean, and the proportion is far higher among the AI/ML categories than among the471others. Large language models have the highest Gini of any category in every year from 2019 onward (the472implausible 2023 value of formal verification apart), and theirs ends the baseline above where it began,473which 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 single474post-period cohort whose window is affected by truncation, the uncited share of that cohort rises by about475the same amount in both groups, so the difference between them is a tail effect rather than a zeros effect,476and the small categories, together with the implausible 2023 value for formal verification, show the477sensitivity of a within-category Gini to a single misattributed record478(Section~\ref{sec:net-topcited}). The 2024 cohort, whose window closes at the end of 2026, will be the first479test with two post-period cohorts.480The reader should also weigh the finding of \citet{nielsen2021inequality} that global citation inequality has481risen over several decades when measured on long windows across all fields; the three-year windows used here482measure a different quantity, early attention, whose inequality is driven by zeros, and the two results are483not in contradiction.484485\begin{figure}[htbp]486\centering487\includegraphics[width=0.95\textwidth]{fig_citation_inequality.pdf}488\caption{Fixed-window citation levels and inequality by publication year, for years with a complete48936-month window. Left: mean $c^{(36)}$ and the 99th percentile divided by ten. Right: Gini coefficient of490$c^{(36)}$ and share of works uncited at 36 months. Source:491\texttt{results/bibliometrics/citation\_windows\_yearly.csv}.}492\label{fig:citation_inequality}493\end{figure}494495The field-weighted citation impact supplied by OpenAlex, reported for comparison in496Table~\ref{tab:citation_windows}, has a mean above one in every year, which says that the eligible corpus is497cited above the OpenAlex world average for works of the same type, year and subfield; its median is below498one in every year, which says that the typical computer-science work is not. The two statements together499are the skewness result once more. The mean FWCI declines slowly, though not monotonically, across cohorts and the median rises through5002022 and collapses for 2025 and 2026, where the exposure is too short for the indicator to mean anything;501the methodology's reservations about FWCI (Section~\ref{sec:m-bibliometrics}) are borne out and the502indicator is not used further.503504\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_citation_windows}\endgroup505\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_net_category_gini}\endgroup506\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{2.5pt}\input{tables/tab_net_gini_ai_vs_rest}\endgroup507508\subsection{The most cited works and what they reveal about the database}509\label{sec:net-topcited}510511Table~\ref{tab:top_cited} lists the ten works with the largest $c^{(36)}$ in each publication year from 2018512to 2025, with their total citations to date. The list is reported because research question RQ3 asks for the513most influential contributions and because the mandate requires that the manuscript identify them; it is514reported with its errors visible because the errors are instructive. Three kinds of entry appear. The first515is the expected one: the foundational works of the deep-learning decade are present with the citation counts516one would expect, among them \emph{Deep Contextualized Word Representations}, \emph{MobileNetV2} and517\emph{Squeeze-and-Excitation Networks} for 2018, \emph{BERT} for 2019, \emph{Momentum Contrast} and518\emph{A Simple Framework for Contrastive Learning} for 2020, the \emph{Vision Transformer} and the519\emph{Swin Transformer} for 2021, \emph{High-Resolution Image Synthesis with Latent Diffusion Models} and520\emph{Masked Autoencoders Are Scalable Vision Learners} for 2022, \emph{Segment Anything} and521\emph{YOLOv7} for 2023, and \emph{DeepSeek-R1} for 2025, together with the scientific-software and522bioinformatics-resource papers (SciPy, NumPy, STRING, SWISS-MODEL, iTOL, AlphaFold Protein Structure523Database, UniProt, KEGG) that the OpenAlex topic classification places in computer science and that are524among the most cited works of any field.525526The second kind of entry is a duplicate or misdated record of a canonical work: \emph{Bitcoin: A Peer-to-Peer527Electronic Cash System} appears as an SSRN record dated 2019 and again dated 2022, \emph{Generative528Adversarial Nets} as a 2023 book chapter, \emph{Batch Normalization} as a 2024 preprint, \emph{Learning529Multiple Layers of Features from Tiny Images} as a 2024 article, and \emph{Attention Is All You Need} as a 2025530preprint. These are not errors of this study's deduplication, which merges a preprint with its published531version within the window (Section~\ref{sec:m-dedup}); they are distinct OpenAlex works, with their own532identifiers and their own citation counts, created when a reference string resolved to a new record rather533than to the existing one, and dated by the record rather than by the work. Their $c^{(36)}$ is large because534the citations of a canonical work accrue to whichever record the citing works' reference strings resolve to.535The third kind is the inconsistent record: entries whose window count exceeds their total count, or whose536total count is zero while their window count is in the thousands, including several records of the Dagstuhl537DROPS series and of regional journals whose titles bear no relation to the citation volume attached to538them. These are, to the best of the author's understanding, artefacts of OpenAlex's reference matching,539where a frequently cited string has been mapped to a wrong target; they are recognisable precisely because540the two counts disagree, and \citet{alperin2024openalex} and \citet{culbert2025openalexcoverage} document541related inconsistencies in OpenAlex citation data at the aggregate level.542543The consequences for this part are limited but must be stated. The aggregate citation statistics of the544previous subsection are insensitive to a small number of misattributed records among hundreds of545thousands per year, except through the maximum and the 99th percentile, which Table~\ref{tab:citation_windows} reports and546which should not be interpreted. The identification of the most influential works for RQ3, by contrast,547cannot rely on a ranked list from the database without a record-level audit, and the audit must check the548consistency of window and total counts, the uniqueness of the work across records, and the agreement of the549record's date with the work's first appearance. That audit is part of the human-review checkpoint on RQ3 and550is \pending{record-level audit of the top-cited lists}; until it is done, the titles above are quoted as what551the database returns, not as a ranking endorsed by this study. (This item does not depend on the552classification and remains open; it belongs to the RQ3 human-review checkpoint, not to the corpus pipeline.) The lesson for the field-normalised scores553of Section~\ref{sec:m-citations} is the same as the one \citet{waltman2016review} draw for all mean-based554indicators: a reference class containing one record with tens of thousands of misattributed citations has a555mean that is wrong for every work in the class, and the normalised scores of Part~IX should be computed556after the exclusion of records failing the consistency check; whether the current pipeline applies that557exclusion is \pending{NCS computed after exclusion of inconsistent records}. (Also left open: the558category-level mean normalised scores of \texttt{category\_impact\_yearly.csv} are computed on the unaudited559reference classes and are for that reason not reported in this part.)560561\begingroup\footnotesize\setlength{\tabcolsep}{4pt}\input{tables/tab_top_cited}\endgroup562563\section{Knowledge inflows and the age of cited work}564\label{sec:net-flows}565566\subsection{Where the references of computer science point}567\label{sec:net-flows-fields}568569Research question RQ4 asks how citation networks and interdisciplinary knowledge flows have evolved, and570H4 predicts that the share of citations crossing area boundaries rises in the post period. The methodology571defines two levels at which flows are measured: between the taxonomy categories of this study, through the572flow matrices of equation~\eqref{eq:flow}, and between the corpus and the rest of the literature, through the573external edge set of Section~\ref{sec:m-citgraph}, whose cited works are typed by their OpenAlex field. Only574the second level is available at the time of writing. Figure~\ref{fig:field_inflows} and575Table~\ref{tab:field_flows} are generated from the current graph tables of \texttt{results/graph/}576(\texttt{field\_flows\_yearly.csv}, corpus v3), and Table~\ref{tab:reference_coverage}, from577\texttt{reference\_coverage\_yearly.csv}, gives the denominators on which every share in this section rests:578the declared references of the eligible works of each citing year, the share of them that resolve to an579OpenAlex record, and the split of the resolved references into internal and external edges.580581\begin{figure}[htbp]582\centering583\includegraphics[width=0.95\textwidth]{fig_field_inflows.pdf}584\caption{Share of the resolved references of eligible works, by citing year, that point to works inside the585corpus and to works outside it by cited OpenAlex field (seven largest external fields). Generated by586\texttt{figures/make\_figures.py} from \texttt{results/graph/field\_flows\_yearly.csv} (corpus v3); the587values are in Table~\ref{tab:field_flows}.}588\label{fig:field_inflows}589\end{figure}590591Table~\ref{tab:reference_coverage} is read first because it conditions the rest. The number of declared592references per eligible work rises through the baseline and falls again in the last three citing years, the5932026 row being the shortest; this is the right-truncation of reference lists (recent records are indexed594before their reference lists are complete) rather than a change in citing practice, and it means that the595shares of the last two rows of every table in this section are computed on fewer references per work than596the earlier rows. The share of declared references that resolve to an OpenAlex record is nearly constant597from 2018 to 2024 and higher in 2025--2026; the recent cohorts carry fewer parsed references per work (the598reference-extraction channels of OpenAlex lag publication), and the references that are already parsed for599them resolve more often. The difference describes how the database was assembled, not what authors cite, and600it is the reason the flow statistics are expressed as shares of resolved references, as the methodology requires.601The internal share of resolved references rises steeply with the citing year, and this is the mechanical602feature of Figure~\ref{fig:field_inflows} that must be read before any other: the corpus starts in 2018, so a603work published in 2018 cannot cite inside it except at age zero, whereas a work published in 2026 has eight604years of corpus to cite. The share of references pointing to computer science outside the corpus, which is605mostly pre-2018 computer science, falls as the internal share rises.606607The two computer-science columns of Table~\ref{tab:field_flows} do not, however, sum to a constant. Their608sum, the share of references that stay within the field, rises in every citing year of the window, and its609complement, the share of references that cross into another OpenAlex field (column `Other fields'), falls in610every year, in the baseline years as in the post years and at a comparable pace on either side of the 2022611boundary. Engineering, the largest external field, accounts for the greater part of the decline;612mathematics, decision sciences, physics and psychology decline slowly; the social sciences are stable; and613medicine is the only field among the seven whose share rises, so that by the end of the window it is the614second largest external destination after engineering. On this evidence the field-level version of H4 is615not supported: the boundary-crossing share of computer-science references toward other fields does not rise616after 2022, it continues to fall, and no change of pace is visible at the boundary.617618Two reservations qualify the direction, though not the absence of a break. The first is a classification619boundary. The eligible corpus is the CS core of Part~III, that is, works with a computer-science topic620whatever their primary field, so a post-2018 engineering work with a computer-science topic is an internal621edge while its pre-2018 counterpart is an external edge typed as engineering; as the corpus lengthens, part622of what used to be counted as a flow to engineering or mathematics is re-counted as internal, and the623decline of the external shares is to that extent mechanical. The field-flow file does not type internal624edges by the cited work's primary field, so the size of this effect cannot be removed here; a flow table625that types every resolved reference, internal or external, by primary field would be the correction, and it626is noted for the director. The second is that H4 concerns boundaries \emph{within} computer science627(systems toward AI, security toward AI, human--computer interaction toward AI), and a field whose sub-areas628converge on a common set of methods may well cite less outside the field, not more, as its internal629frontier absorbs the attention that used to go to engineering or mathematics. A falling external share is630therefore compatible with H4 and with its negation, and only the category flow matrices can decide between631them. What the field-level table does establish is a boundary condition for the interdisciplinarity632literature: the diversity indices of Section~\ref{sec:m-diversity}, whether Rao--Stirling or633Leinster--Cobbold, are computed over a reference distribution whose external component is shrinking634smoothly, so that any change they detect at the 2022 boundary will come from the internal component.635\citet{porter2009interdisciplinarity} found, for six fields over three decades, that interdisciplinarity636measured on references rose slowly and mostly through neighbouring fields; the computer-science columns show637the neighbouring fields (engineering, mathematics, decision sciences) losing share and a non-neighbouring638one (medicine) gaining it, and they do not show the acceleration that the foundation-model narrative would639predict.640641\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3pt}\input{tables/tab_reference_coverage}\endgroup642643\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{2.5pt}\input{tables/tab_field_flows}\endgroup644645\subsection{The age of cited work}646\label{sec:net-age}647648The age of the works a field cites is the simplest measure of how fast its knowledge turns over, and the649literature disagrees on its direction. \citet{evans2008narrowing} reported that online availability narrowed650citation toward fewer and more recent works; \citet{verstak2014giants}, in a preprint based on Google Scholar,651reported the opposite, a growing share of citations to older articles; \citet{parolo2015attention} measured652an accelerating decay of attention to individual papers as the volume of publication grew; and653\citet{chu2021slowed} argued that in very large fields the growth of publication itself ossifies the canon,654because new work cannot be read widely enough to displace it. Computer science is the field in which the655turnover is expected to be fastest, and \citet{frank2019citationgraphs} found that the AI citation graph had656become more self-referential and more recent-leaning over the 2010s.657658Figure~\ref{fig:cited_age} and Table~\ref{tab:cited_age} give the distribution of the age of cited works, the659citing year minus the cited work's publication year, for the resolved references of eligible works, read660from the corpus v3 file \texttt{results/\allowbreak graph/\allowbreak cited\_age\_yearly.csv}, which is built on the same edge sets as661Table~\ref{tab:reference_coverage}. The mode of citation age is two years in every citing year (visible in662the figure, where every curve peaks at the same abscissa); the mean age falls in every citing year from 2018663to 2026; the median falls over the baseline years and is constant from 2021 onward; the share of664references to works at most five years old rises by roughly the amount by which the share of references to665works more than ten years old falls; and the share of references to works at most two years old rises less,666and mostly during the baseline years. The shift is steady and does not accelerate at the 2022 boundary; the667post-period curves in the figure continue the movement of the baseline curves, and the year-to-year changes668of the mean in the table are of the same order before and after it, if anything smaller after. A small share of references point to669works dated after the citing work, which arises from preprints cited before their published version carries670a later date and from year-only dates; this share falls to zero over the window as the corpus's own dates671become first-appearance dates, and it is excluded from the age statistics.672673\begin{figure}[htbp]674\centering675\includegraphics[width=0.95\textwidth]{fig_cited_age.pdf}676\caption{Distribution of the age of cited works (citing year minus cited year, 0 to 30 years) for five677citing years. Generated by \texttt{figures/make\_figures.py} from678\texttt{results/\allowbreak graph/\allowbreak cited\_age\_yearly.csv} (corpus v3); summary statistics in Table~\ref{tab:cited_age}.}679\label{fig:cited_age}680\end{figure}681682The evidence therefore sides with \citet{evans2008narrowing} and \citet{parolo2015attention} rather than683with \citet{verstak2014giants} for this field and this window, with one reservation that the reference684coverage of OpenAlex imposes. If the probability that a reference string resolves to an OpenAlex record is685higher for recent, DOI-bearing works than for older ones, as \citet{culbert2025openalexcoverage} report in686their comparison with Web of Science and Scopus, then the resolved references are biased toward youth, and a687constant true age distribution would appear to become younger as the resolvable share rises.688Table~\ref{tab:reference_coverage} is the control. The resolved share is nearly constant from 2018 to 2024,689so over those years a resolution bias toward recent works would shift the level of the age distribution but690not its trend; the fall of the mean and of the over-ten-year share between 2018 and 2024 is therefore not an691artefact of a rising resolvable share. The 2025 and 2026 rows are different: their resolved share is higher692and their reference lists shorter (right-truncation), and the small further decline of the mean age in those693two rows should not be read on its own. The age shift is reported here as observed within the resolved694references, not as corrected for the composition of the unresolved ones, which cannot be typed.695696\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_cited_age}\endgroup697698\subsection{Knowledge flows between categories}699\label{sec:net-flows-categories}700701The flow matrices $F_t$ between the categories of the ontology, the cross-area shares $X_{\alpha,t}$ of702equation~\eqref{eq:cross-area} and the yearly modularities $Q_{\mathrm{cat}}$ and $Q_{\mathrm{area}}$ of703equation~\eqref{eq:modularity} are the statistics on which H4 turns. They require the primary category of704every work, which the classification of Part~IX supplies, and they are computed by705\texttt{knowledge\_graph/02\_category\_flows.py} on the internal edges of Section~\ref{sec:m-citgraph},706that is, on references from eligible works to eligible works with a primary category at both ends.707Two properties of this edge set govern everything that follows. First, the internal network is small in7082018 and grows with every citing year, because the corpus begins in 2018 and a citing year can only cite709the corpus years that precede it; the 2018 row of every table below describes a network of references to710works of the same year and is not comparable with the later rows, so the series effectively begin in 2019.711Second, the restriction to internal references means that an area's flows are measured over its references712to \emph{recent} computer science only; references to older work and to other fields, which713Sections~\ref{sec:net-flows-fields} and~\ref{sec:net-age} showed to be a declining share, are outside the714matrix. Table~\ref{tab:net_area_flows} and Figure~\ref{fig:area_flow_matrix} give the area flow matrices715by period, Table~\ref{tab:net_category_to_ai} the share of each category's internal references that go to716the nine categories of the AI/ML area, and Table~\ref{tab:net_modularity} and717Figure~\ref{fig:cross_area} the cross-area shares and the modularities by year.718719\begin{figure}[htbp]720\centering721\includegraphics[width=0.95\textwidth]{fig_area_flow_matrix.pdf}722\caption{Citation-flow matrices between the eight areas of the ontology, baseline (citing years7232018--2022) and post (2023--2026) periods: row shares of internal references from the citing area (rows)724to the cited area (columns), per cent. Source: \texttt{results/graph/area\_flows\_yearly.csv}.}725\label{fig:area_flow_matrix}726\end{figure}727728The area matrices are diagonal-dominant in both periods: every area but one sends the majority of its729internal references to itself, from about two thirds for the security, software, theory and730computational-science areas to a much higher share for the perception area, which is the largest area and the one whose categories (vision, language, speech,731robotics, interaction, graphics) cite each other most. The largest off-diagonal flows are structural and do732not change between periods: the AI/ML area sends about a third of its references to the perception area,733which is where the application work on vision and language that the machine-learning categories build on734is classified; the security area sends about a sixth of its references to the data and distributed area, the735networks and cloud work that security builds on; and computational science splits its outside references736between AI/ML and perception. What changes between periods is the AI/ML column. The self-share of every737area except perception and hardware falls, and the share of references each area sends to the AI/ML area rises,738the increments being largest for the software area, computational science, security and the data and739distributed area (Table~\ref{tab:net_area_flows}; the post-minus-baseline differences are the subject of740Part~IX). The AI/ML area's own self-share falls as well, in favour of the perception area: the741machine-learning categories cite vision and language work more in the post period than before, which is the742flow one expects when the models of the post period are evaluated on the tasks of those categories. The743perception area is the exception on both counts: its self-share is the same in the two periods and its744share of references to the AI/ML area changes little, so the convergence that the AI/ML column shows is a745convergence of the smaller areas toward AI, not of the largest.746747The category-level table (Table~\ref{tab:net_category_to_ai}) tests H4 at the resolution at which it is748stated, since the hypothesis names systems, security and human--computer interaction as the citing fields749that should cite the AI categories more. All three do. The share of references going to the AI/ML area750rises in human--computer interaction, software engineering, cybersecurity, database systems, distributed751computing, computer networks and computer architecture, in each case from the beginning of the window,752and in each case the values of 2024 and 2025 are at or above every baseline value. The timing differs across these753series in a way the hypothesis does not predict. For human--computer interaction the series is nearly flat754through 2023 and rises steeply in 2024, 2025 and the incomplete 2026; for software engineering the rise755begins in 2021 and steepens from 2023; in both the change is concentrated in the second and third756post-period years rather than at the boundary, consistent757with the lag between the appearance of a model and the appearance of empirical work that cites it; for758cybersecurity, database systems and distributed computing the post-period increments continue the baseline759pace; for computer networks and computer architecture the share is the lowest among the systems categories760and its rise is slight. Within the perception area, natural language processing is the category with the761largest post-period change of any in the table: its share of references to the AI/ML area falls from 2018762to 2020, which is the period in which the pre-trained language model became the standard tool of the763category and was cited as NLP work rather than as machine learning, and rises steeply from 2023, as the764large-language-model category (which the ontology places in the AI/ML area) absorbs the work the category765now builds on. Computer vision shows no such rise, which again reflects the classifier's boundary: vision766work citing vision models is a within-category flow. The theory categories rise modestly, and767computational biology and robotics return in the post period to the levels of the earliest, sparse years. These are768flows of references between classified works; they say that the systems, security and interaction769categories build on AI/ML-classified work more than they did, which is what H4 asserts, and not that the770work itself has become AI research, which is a question about classification rather than citation.771772\begin{figure}[htbp]773\centering774\includegraphics[width=0.95\textwidth]{fig_cross_area.pdf}775\caption{Left: share of internal references leaving the citing area, $X_{\alpha,t}$ of776equation~\eqref{eq:cross-area}, by citing area and year (per cent). Right: modularity of the yearly777category citation-flow network at the area and category partitions (equation~\eqref{eq:modularity}) and the778within-category self-share. Sources: \texttt{results/graph/cross\_area\_share\_yearly.csv},779\texttt{results/graph/modularity\_yearly.csv}. 2026 is incomplete.}780\label{fig:cross_area}781\end{figure}782783The cross-area shares (Figure~\ref{fig:cross_area}, left; the yearly values by area are in Part~IX) order784the areas by how much of their citation leaves them. The AI/ML area has the highest boundary-crossing rate785in every year and the rate rises through 2022 and is flat thereafter; its position at the top is a786consequence of where the ontology draws its boundaries, since the area's two largest partners, vision and787language, are placed in a different area, and the statistic would be lower under any ontology that grouped788machine learning with its application fields. This dependence on the partition is the reason789Section~\ref{sec:m-networks} describes $X_{\alpha,t}$ as a boundary-crossing rate and not as a measure of790interdisciplinarity in the sense of \citet{stirling2007diversity} or \citet{rafols2010diversity}, whose791indicators weight pairs of categories by their distance. The security, software and data areas792rise through the whole window; the theory area rises in the sparse early years, is flat in the late793baseline and rises again in the post period; the hardware area is flat, computational science rises and794falls back in the incomplete year, and the perception area, after a fall in 2019 that belongs to the small7952018 network, is flat at the lowest level. Table~\ref{tab:net_modularity} aggregates these shares over areas796in two ways. The raw aggregate is flat through the baseline and rises in every post-period year; the797composition-adjusted aggregate, which holds the weights of the citing areas at their baseline values, rises798by less, so part of the post-period rise of the raw series is the growing weight among citing works of the799AI/ML area, which is the most boundary-crossing area, and the remainder, which is positive in every800post-period year, is a within-area rise of boundary crossing. H4's first component, that the share of801citations crossing area boundaries rises in the post period, is supported on both the raw and the adjusted802series, with the composition qualification stated.803804H4's second component is the modularity. $Q_{\mathrm{cat}}$ peaks in 2019 and falls in every subsequent805year; $Q_{\mathrm{area}}$ falls in every year from 2018 to 2025 and is flat, with a slight uptick in the806incomplete year, from 2023 onward; the self-share peaks in 2019, is nearly flat through 2022 and falls in every post-period year, fastest after 2023807(Table~\ref{tab:net_modularity}, Figure~\ref{fig:cross_area}, right). The post-period means are below the808baseline means at both partitions, as the note of the table records, so the verdict on this component is809that the hypothesis is supported in direction at both levels. The caveats are substantive. The decline is810present throughout the baseline; the 2022 boundary is not a break in either series; the yearly811decrements of $Q_{\mathrm{cat}}$ are somewhat larger in the post period than in the late baseline, while812$Q_{\mathrm{area}}$ stops falling after 2023, so that the two partitions tell different stories about the813post period: continued, slightly faster de-assortment between categories, and an end to the decline between814areas. Because the partition is fixed, a fall in815$Q$ can arise from a change in the mix of citing works as well as from a change in citing behaviour; the816adjusted cross-area series shows that both are present. The modularity of equation~\eqref{eq:modularity}817inherits every property of the classifier, and in particular the placement of large language models in the818AI/ML area and of natural language processing outside it converts the post-period citation of LLM work by819NLP work into a cross-area flow by construction. The internal network grows by an order of magnitude over820the window, so the 2018 and 2019 values describe sparse networks; and the 2026 row is a partial year whose821works carry fewer parsed references. The co-classification matrix of822\texttt{category\_cooccurrence\_yearly.csv}, which counts works carrying two categories in their full label823set, is reported in Part~IX and is not used here, because, as Section~\ref{sec:m-classification} notes, it824responds to abstract length and vocabulary in a way the primary-label flows do not. What the flows and the825modularity together establish is modest and definite: the citation network of recent computer science is826becoming less assortative by category, the change is gradual and began before 2022, and the areas that827have moved are the smaller ones, which cite the machine-learning categories more, while the largest area828cites itself as much as it ever did.829830\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_area_flows}\endgroup831\begingroup\renewcommand{\small}{\scriptsize}\setlength{\tabcolsep}{3pt}\input{tables/tab_net_modularity}\endgroup832\begingroup\scriptsize\setlength{\tabcolsep}{3pt}\input{tables/tab_net_category_to_ai}\endgroup833834\section{The boundary of the database}835\label{sec:net-boundaries}836837\subsection{What DBLP sees that the corpus does not}838839The corpus is the union of several sources resolved to OpenAlex records (Section~\ref{sec:data-linkage}),840and a DBLP record without an OpenAlex counterpart cannot enter it, because the citation, affiliation and841topic data on which every indicator of this part depends are OpenAlex's. Table~\ref{tab:dblp_only} counts842these records by DBLP type and year. They are a small fraction of DBLP's annual output, and their843composition is specific: journal articles with a DOI that OpenAlex has not indexed or has indexed under a844different identifier, conference papers mostly without a DOI, which are the hardest to link by title, and845doctoral theses, which DBLP indexes from a few national repositories and OpenAlex largely does not. The846``data'' type, DBLP's record of datasets and software, grows across the window and is almost entirely847unmatched, which is a reminder that the research outputs of computer science that are not papers are848outside the corpus altogether. For 2026 the conference share of the unmatched records rises sharply, which849is the DBLP-side manifestation of the right truncation discussed in Section~\ref{sec:data-dates}: DBLP850indexes a proceedings volume as a whole when it appears, OpenAlex matches it paper by paper over the851following months, and the gap is largest in the most recent year. The missing records bias the indicators852of this part toward the parts of computer science that publish with DOIs in journals and large conference853series, that is, away from theses, workshop papers and national venues; the direction of the bias is known854and its magnitude is bounded by the table.855856\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_dblp_only}\endgroup857858\subsection{Why the creation date does not measure indexing lag}859860The research plan proposed to estimate the indexing delay of OpenAlex from the \texttt{created\_date} of861each record and to correct the recent months of the publication series for it. Part~III862(Section~\ref{sec:data-dates}) records why the proposal was abandoned; Table~\ref{tab:indexing_lag} gives863the evidence in annual form. For every publication year up to 2024, the median lag between publication and864record creation is of the order of years, it is larger for January than for June publications by almost865exactly five months, and more than nine tenths of the year's records were ``created'' more than 180 days866after publication. A genuine indexing delay cannot have that shape: it would be measured in weeks or867months, would not depend on the month of publication within the year, and would not place nearly all868records beyond the 180-day mark. The shape is that of a single creation date for the bulk of the database,869with the lag equal to the time between each work's publication and that date, which places the date in the870second half of 2025. For works published in 2025 and 2026 the field behaves differently: a large share of871records is created within 90 days of publication, and the median lag collapses to days by mid-2026. The872field therefore measures the delay only for records created after the re-ingestion, and only for them873would a lag profile be meaningful; a profile estimated from the whole table, or from the years that the874structural-change analysis needs for its pre-trend diagnostics, would be an artefact of database875maintenance. This is the reason the structural-change analysis truncates the series rather than correcting876it (Section~\ref{sec:m-truncation}), and it is the reason the only honest estimator of indexing lag is the877comparison of two snapshots of the same database, which the released raw snapshots make possible for a878future study.879880\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_indexing_lag}\endgroup881882\section{Hypotheses H4--H6 at this stage}883\label{sec:net-hypotheses}884885The protocol states its hypotheses with a direction so that null and opposite results are reported as886such. On the evidence of this part, the verdicts are the following, each limited to the component of the887hypothesis that the available tables test.888889H4 (convergence) is supported in direction on both of its components and qualified on both. The share of890internal references crossing area boundaries rises in the post period, on the raw aggregate and on the891composition-adjusted aggregate alike, and the systems, security and interaction categories the hypothesis892names all send a growing share of their references to the AI/ML categories, with the steepest rises for893human--computer interaction and software engineering in 2024--2026 rather than at the boundary894(Tables~\ref{tab:net_category_to_ai} and~\ref{tab:net_modularity}). The modularity falls at both the895category and the area partition, with post-period means below baseline means, but the fall is a896baseline trend that continues, slightly faster, at the category level and stops at the area level after 2023; part of it is897the growing weight of the most boundary-crossing area among citing works, and all of it depends on where the898ontology draws the boundary between machine learning and its application fields899(Section~\ref{sec:net-flows-categories}). The field-level counterpart, the share of computer-science900references that cross into other OpenAlex fields, falls through the window with no change of pace at the901boundary (Table~\ref{tab:field_flows}, Section~\ref{sec:net-flows-fields}), part of the fall being a902mechanical consequence of the corpus boundary; convergence within computer science and a narrowing of its903references outside computer science are therefore observed together.904905H5 (concentration) has two components. The citation-inequality component is stated for AI categories, and906for the one post-period cohort with a complete window the pooled Gini of the AI/ML categories is above its907baseline mean while that of the other categories is below, with most AI/ML categories and a minority of the908others above their baseline means and large language models the most unequal category in every year909(Tables~\ref{tab:net_category_gini} and~\ref{tab:net_gini_ai_vs_rest}); this is the predicted direction, on910one cohort affected by right truncation, with the uncited share rising equally in both groups, so the911evidence is weak and provisional until the 2024 window closes. The aggregate counterpart gives a Gini of912three-year citations that falls through the baseline and rises for that same cohort, a movement dominated by913the share of uncited works and by truncation, and not interpretable as a change in concentration. The venue-concentration914component predicted a stable or lower index once preprints are treated separately; the index with arXiv915included rises, for the mechanical reason the protocol anticipated, and the index without the preprint type916is pending. The non-arXiv venue landscape widens.917918H6 (geography and collaboration) has three components. The international co-authorship share does not919rise, as predicted, and in fact declines slightly, with a composition explanation that the country shares920support. The China share rises in the aggregate under both counting conventions, as predicted, but as the921continuation of a baseline trend; it rises in the AI/ML categories too, by less than in the other categories,922so the specificity the hypothesis asserts is not observed, and the categories that define the post period923(large language models, foundation models, generative AI) are flat or falling924(Tables~\ref{tab:net_category_actors} and~\ref{tab:net_ai_vs_rest}). The industry share does \emph{not}925rise in the aggregate: it peaks in 2021 and declines in every post-period year, which is the opposite of the926predicted direction; the category-specific version is also opposite, with the AI/ML area losing more company927share than the other areas and all of its highest-share categories losing share, part of the decline being928the lower affiliation coverage of preprint-heavy categories, and with the frontier-level measures of the929literature it was drawn from measuring a different object.930931What the part adds beyond the hypotheses is a set of structural observations that were not predicted and932that the interpretation of Part~IX will have to accommodate: the fall in absolute joint output between China933and the United States during a period in which both grew; the stability of the institutional hierarchy; the934rise of generalist repositories among the largest sources of computer-science records; the steady shift of935references toward younger work without acceleration at the boundary; the asymmetry of the category flows,936in which the smaller areas move toward the machine-learning categories while the largest area, perception937and interaction, cites itself as much as before; the late timing of the rise in citation of AI work by938human--computer interaction and software engineering, two to three years after the boundary; and the939record-level artefacts in the most-cited lists, which make any ranking of influential works conditional on940an audit that this part has specified but not performed.941942