| 1 | % part08_networks.tex — Part VIII, Scientific Knowledge Networks (Agent L/I, 2026-11-03). |
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). |
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). |
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). |
| 4 | |
5 | |
| 5 | \section{Scope and reading rules} |
6 | \section{Scope and reading rules} |
| 6 | \label{sec:net-scope} |
7 | \label{sec:net-scope} |
| 20 | OpenAlex-primary-field and arXiv \texttt{cs} works after the exclusions of the PRISMA flow, and the indicators |
21 | OpenAlex-primary-field and arXiv \texttt{cs} works after the exclusions of the PRISMA flow, and the indicators |
| 21 | inherit the boundary decisions and the affiliation completeness of that corpus. Second, the two periods of the |
22 | inherit the boundary decisions and the affiliation completeness of that corpus. Second, the two periods of the |
| 22 | protocol are unequal in length and in completeness: the baseline runs from January 2018 to the end of |
23 | protocol are unequal in length and in completeness: the baseline runs from January 2018 to the end of |
| 23 | −November 2022, the post period from December 2022 to the snapshot of October 2026 completed by the API |
24 | +November 2022, the post period from December 2022 to the snapshot of October 2026 (the API increment of |
| 24 | −increment, and the last year of the post period is partial for the reasons set out in |
25 | +Part~III is archived but not yet merged into the analytical corpus), and the last year of the post period is partial for the reasons set out in |
| 25 | Section~\ref{sec:data-dates}. Tables by year therefore carry 2026 as an incomplete row, and the fixed-window |
26 | Section~\ref{sec:data-dates}. Tables by year therefore carry 2026 as an incomplete row, and the fixed-window |
| 26 | citation statistics of Section~\ref{sec:net-citations} are complete only up to the publication years flagged in |
27 | citation statistics of Section~\ref{sec:net-citations} are complete only up to the publication years flagged in |
| 27 | Table~\ref{tab:citation_windows}. Third, the comparison of periods is descriptive. The protocol states the |
28 | Table~\ref{tab:citation_windows}. Third, the comparison of periods is descriptive. The protocol states the |
| 401 | citing population produces: each publication year is cited by the following two years' output, and that output |
402 | citing population produces: each publication year is cited by the following two years' output, and that output |
| 402 | grows, so later cohorts receive more citations at equal exposure \citep{bornmann2015growth}. The reversal in |
403 | grows, so later cohorts receive more citations at equal exposure \citep{bornmann2015growth}. The reversal in |
| 403 | 2023 is the first sign of right truncation in the window, since the third calendar year of the 2023 cohort |
404 | 2023 is the first sign of right truncation in the window, since the third calendar year of the 2023 cohort |
| 404 | −is 2025, for which the increment of Part~III is complete but the slower channels of indexing are not; it is |
405 | +is 2025, for which the slower channels of indexing (and citation extraction) are not complete; it is |
| 405 | flagged in the table and is the reason the 2024 row, whose window is formally incomplete, is not used. |
406 | flagged in the table and is the reason the 2024 row, whose window is formally incomplete, is not used. |
| 406 | |
407 | |
| 407 | The Gini coefficient of $c^{(36)}$ is the inequality statistic named, with a deviation in window length |
408 | The Gini coefficient of $c^{(36)}$ is the inequality statistic named, with a deviation in window length |
| 506 | defines two levels at which flows are measured: between the taxonomy categories of this study, through the |
507 | defines two levels at which flows are measured: between the taxonomy categories of this study, through the |
| 507 | flow matrices of equation~\eqref{eq:flow}, and between the corpus and the rest of the literature, through the |
508 | flow matrices of equation~\eqref{eq:flow}, and between the corpus and the rest of the literature, through the |
| 508 | external edge set of Section~\ref{sec:m-citgraph}, whose cited works are typed by their OpenAlex field. Only |
509 | external edge set of Section~\ref{sec:m-citgraph}, whose cited works are typed by their OpenAlex field. Only |
| 509 | −the second level is available at the time of writing, and only from the first version of the corpus: the |
510 | +the second level is available at the time of writing. Figure~\ref{fig:field_inflows} and |
| 510 | −graph tables of \texttt{results/graph/} are being regenerated for corpus v2, and the field-flow file was not |
511 | +Table~\ref{tab:field_flows} are generated from the current graph tables of \texttt{results/graph/} |
| 511 | −present when this part was written. Figure~\ref{fig:field_inflows}, generated from the v1 file, is |
512 | +(\texttt{field\_flows\_yearly.csv}, corpus v3), and Table~\ref{tab:reference_coverage}, from |
| 512 | −described here qualitatively, and every quantitative statement about it is \pending{v2 graph}. |
513 | +\texttt{reference\_coverage\_yearly.csv}, gives the denominators on which every share in this section rests: |
| |
514 | +the declared references of the eligible works of each citing year, the share of them that resolve to an |
| |
515 | +OpenAlex record, and the split of the resolved references into internal and external edges. |
| 513 | |
516 | |
| 514 | \begin{figure}[htbp] |
517 | \begin{figure}[htbp] |
| 515 | \centering |
518 | \centering |
| 516 | \includegraphics[width=0.95\textwidth]{fig_field_inflows.pdf} |
519 | \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 the |
520 | \caption{Share of the resolved references of eligible works, by citing year, that point to works inside the |
| 518 | −corpus and to works outside it by cited OpenAlex field (seven largest external fields). Generated from the |
521 | +corpus and to works outside it by cited OpenAlex field (seven largest external fields). Generated by |
| 519 | −corpus v1 file \texttt{results/graph/field\_flows\_yearly.csv}; to be regenerated for v2.} |
522 | +\texttt{figures/make\_figures.py} from \texttt{results/graph/field\_flows\_yearly.csv} (corpus v3); the |
| |
523 | +values are in Table~\ref{tab:field_flows}.} |
| 520 | \label{fig:field_inflows} |
524 | \label{fig:field_inflows} |
| 521 | \end{figure} |
525 | \end{figure} |
| 522 | |
526 | |
| 523 | −The figure separates the references of each citing year into those that point inside the corpus, that is, to |
527 | +Table~\ref{tab:reference_coverage} is read first because it conditions the rest. The number of declared |
| 524 | −computer-science works published from 2018 onward, and those that point outside it, by the cited work's |
528 | +references per eligible work rises through the baseline and falls again in the last three citing years, the |
| 525 | −field. Its dominant feature is mechanical and must be read first: the share of references pointing inside the |
529 | +2026 row being the shortest; this is the right-truncation of reference lists (recent records are indexed |
| 526 | −corpus rises steeply with the citing year, and the share pointing to computer science outside the corpus |
530 | +before their reference lists are complete) rather than a change in citing practice, and it means that the |
| 527 | −falls by the same amount, because the corpus starts in 2018 and a work published in 2018 cannot cite inside |
531 | +shares of the last two rows of every table in this section are computed on fewer references per work than |
| 528 | −it except at age zero, whereas a work published in 2026 has eight years of corpus to cite. The two |
532 | +the earlier rows. The share of declared references that resolve to an OpenAlex record is nearly constant |
| 529 | −computer-science curves together are approximately flat, and their sum is the share of references that |
533 | +from 2018 to 2024 and higher in 2025--2026; the recent cohorts carry fewer parsed references per work (the |
| 530 | −stay within the field. The curves of the other fields are what the flow question is about, and they are |
534 | +reference-extraction channels of OpenAlex lag publication), and the references that are already parsed for |
| 531 | −nearly flat over the window: engineering is the largest external field and declines slowly, the social |
535 | +them resolve more often. The difference describes how the database was assembled, not what authors cite, and |
| 532 | −sciences, mathematics, medicine, psychology and decision sciences each hold a few per cent of references |
536 | +it is the reason the flow statistics are expressed as shares of resolved references, as the methodology requires. |
| 533 | −with no visible change of direction in the post period, and medicine is the only external field whose share |
537 | +The internal share of resolved references rises steeply with the citing year, and this is the mechanical |
| 534 | −rises slightly at the end of the window. On the v1 evidence the field-level version of H4 is not supported: |
538 | +feature of Figure~\ref{fig:field_inflows} that must be read before any other: the corpus starts in 2018, so a |
| 535 | −the boundary-crossing share of computer-science references toward other OpenAlex fields does not rise |
539 | +work published in 2018 cannot cite inside it except at age zero, whereas a work published in 2026 has eight |
| 536 | −after 2022, and the slow decline of the engineering share continues a trend visible in the baseline. |
540 | +years of corpus to cite. The share of references pointing to computer science outside the corpus, which is |
| 537 | − |
541 | +mostly pre-2018 computer science, falls as the internal share rises. |
| 538 | −This is a weaker statement than the one H4 makes, and the difference should be kept in view. The |
542 | + |
| 539 | −hypothesis concerns boundaries \emph{within} computer science (systems toward AI, security toward AI, |
543 | +The two computer-science columns of Table~\ref{tab:field_flows} do not, however, sum to a constant. Their |
| 540 | −human--computer interaction toward AI), and a field whose sub-areas converge on a common set of methods |
544 | +sum, the share of references that stay within the field, rises in every citing year of the window, and its |
| 541 | −may well cite less outside the field, not more, as its internal frontier absorbs the attention that used to |
545 | +complement, the share of references that cross into another OpenAlex field (column `Other fields'), falls in |
| 542 | −go to mathematics or engineering. The flat external shares are therefore compatible with H4 and with its |
546 | +every year, in the baseline years as in the post years and at a comparable pace on either side of the 2022 |
| 543 | −negation, and only the category flow matrices can decide between them. What the field-level curves do |
547 | +boundary. Engineering, the largest external field, accounts for the greater part of the decline; |
| 544 | −establish is a boundary condition for the interdisciplinarity literature: the diversity indices of |
548 | +mathematics, decision sciences, physics and psychology decline slowly; the social sciences are stable; and |
| 545 | −Section~\ref{sec:m-diversity}, whether Rao--Stirling or Leinster--Cobbold, will be computed over a reference |
549 | +medicine is the only field among the seven whose share rises, so that by the end of the window it is the |
| 546 | −distribution whose external component is small and stable, so that any change they detect will come from |
550 | +second largest external destination after engineering. On this evidence the field-level version of H4 is |
| 547 | −the internal component. \citet{porter2009interdisciplinarity} found, for six fields over three decades, that |
551 | +not supported: the boundary-crossing share of computer-science references toward other fields does not rise |
| 548 | −interdisciplinarity measured on references rose slowly and mostly through neighbouring fields; the |
552 | +after 2022, it continues to fall, and no change of pace is visible at the boundary. |
| 549 | −computer-science curves are consistent with that pattern and do not show the acceleration that the |
553 | + |
| 550 | −foundation-model narrative would predict. |
554 | +Two reservations qualify the direction, though not the absence of a break. The first is a classification |
| |
555 | +boundary. The eligible corpus is the CS core of Part~III, that is, works with a computer-science topic |
| |
556 | +whatever their primary field, so a post-2018 engineering work with a computer-science topic is an internal |
| |
557 | +edge while its pre-2018 counterpart is an external edge typed as engineering; as the corpus lengthens, part |
| |
558 | +of what used to be counted as a flow to engineering or mathematics is re-counted as internal, and the |
| |
559 | +decline of the external shares is to that extent mechanical. The field-flow file does not type internal |
| |
560 | +edges by the cited work's primary field, so the size of this effect cannot be removed here; a flow table |
| |
561 | +that types every resolved reference, internal or external, by primary field would be the correction, and it |
| |
562 | +is noted for the director. The second is that H4 concerns boundaries \emph{within} computer science |
| |
563 | +(systems toward AI, security toward AI, human--computer interaction toward AI), and a field whose sub-areas |
| |
564 | +converge on a common set of methods may well cite less outside the field, not more, as its internal |
| |
565 | +frontier absorbs the attention that used to go to engineering or mathematics. A falling external share is |
| |
566 | +therefore compatible with H4 and with its negation, and only the category flow matrices can decide between |
| |
567 | +them. What the field-level table does establish is a boundary condition for the interdisciplinarity |
| |
568 | +literature: the diversity indices of Section~\ref{sec:m-diversity}, whether Rao--Stirling or |
| |
569 | +Leinster--Cobbold, are computed over a reference distribution whose external component is shrinking |
| |
570 | +smoothly, so that any change they detect at the 2022 boundary will come from the internal component. |
| |
571 | +\citet{porter2009interdisciplinarity} found, for six fields over three decades, that interdisciplinarity |
| |
572 | +measured on references rose slowly and mostly through neighbouring fields; the computer-science columns show |
| |
573 | +the neighbouring fields (engineering, mathematics, decision sciences) losing share and a non-neighbouring |
| |
574 | +one (medicine) gaining it, and they do not show the acceleration that the foundation-model narrative would |
| |
575 | +predict. |
| |
576 | + |
| |
577 | +\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3pt}\input{tables/tab_reference_coverage}\endgroup |
| |
578 | + |
| |
579 | +\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{2.5pt}\input{tables/tab_field_flows}\endgroup |
| 551 | |
580 | |
| 552 | \subsection{The age of cited work} |
581 | \subsection{The age of cited work} |
| 553 | \label{sec:net-age} |
582 | \label{sec:net-age} |
| 563 | become more self-referential and more recent-leaning over the 2010s. |
592 | become more self-referential and more recent-leaning over the 2010s. |
| 564 | |
593 | |
| 565 | Figure~\ref{fig:cited_age} and Table~\ref{tab:cited_age} give the distribution of the age of cited works, the |
594 | Figure~\ref{fig:cited_age} and Table~\ref{tab:cited_age} give the distribution of the age of cited works, the |
| 566 | −citing year minus the cited work's publication year, for the resolved references of eligible works. The |
595 | +citing year minus the cited work's publication year, for the resolved references of eligible works, read |
| 567 | −cited-age file is the one graph table available at the time of writing, and it is a v1 file; the table will |
596 | +from the corpus v3 file \texttt{results/graph/cited\_age\_yearly.csv}, which is built on the same edge sets as |
| 568 | −be regenerated from the v2 file by the same script and its values are \pending{v2 graph}. On the v1 |
597 | +Table~\ref{tab:reference_coverage}. The mode of citation age is two years in every citing year (visible in |
| 569 | −distribution, the mode of citation age is two years in every citing year, the mean falls monotonically from |
598 | +the figure, where every curve peaks at the same abscissa); the mean age falls in every citing year from 2018 |
| 570 | −2018 to 2025, the median falls from six to five years, the share of references to works at most five years |
599 | +to 2026; the median falls over the baseline years and is constant from 2021 onward; the share of |
| 571 | −old rises by more than ten points over the window, and the share to works more than ten years old falls by |
600 | +references to works at most five years old rises by roughly the amount by which the share of references to |
| 572 | −about the same amount. The shift is steady and does not accelerate at the 2022 boundary; the post-period |
601 | +works more than ten years old falls; and the share of references to works at most two years old rises less, |
| 573 | −curves in the figure continue the movement of the baseline curves. A small share of references point to |
602 | +and mostly during the baseline years. The shift is steady and does not accelerate at the 2022 boundary; the |
| |
603 | +post-period curves in the figure continue the movement of the baseline curves, and the year-to-year changes |
| |
604 | +of the mean in the table are of the same order before and after it, if anything smaller after. A small share of references point to |
| 574 | works dated after the citing work, which arises from preprints cited before their published version carries |
605 | works dated after the citing work, which arises from preprints cited before their published version carries |
| 575 | −a later date and from year-only dates; this share falls over the window as the corpus's own dates become |
606 | +a later date and from year-only dates; this share falls to zero over the window as the corpus's own dates |
| 576 | −first-appearance dates, and is excluded from the age statistics. |
607 | +become first-appearance dates, and it is excluded from the age statistics. |
| 577 | |
608 | |
| 578 | \begin{figure}[htbp] |
609 | \begin{figure}[htbp] |
| 579 | \centering |
610 | \centering |
| 580 | \includegraphics[width=0.95\textwidth]{fig_cited_age.pdf} |
611 | \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 five |
612 | \caption{Distribution of the age of cited works (citing year minus cited year, 0 to 30 years) for five |
| 582 | −citing years. Generated from the corpus v1 file \texttt{results/graph/cited\_age\_yearly.csv}; to be |
613 | +citing years. Generated by \texttt{figures/make\_figures.py} from |
| 583 | −regenerated for v2.} |
614 | +\texttt{results/graph/cited\_age\_yearly.csv} (corpus v3); summary statistics in Table~\ref{tab:cited_age}.} |
| 584 | \label{fig:cited_age} |
615 | \label{fig:cited_age} |
| 585 | \end{figure} |
616 | \end{figure} |
| 586 | |
617 | |
| 589 | coverage of OpenAlex imposes. If the probability that a reference string resolves to an OpenAlex record is |
620 | coverage of OpenAlex imposes. If the probability that a reference string resolves to an OpenAlex record is |
| 590 | higher for recent, DOI-bearing works than for older ones, as \citet{culbert2025openalexcoverage} report in |
621 | higher for recent, DOI-bearing works than for older ones, as \citet{culbert2025openalexcoverage} report in |
| 591 | their comparison with Web of Science and Scopus, then the resolved references are biased toward youth, and a |
622 | their comparison with Web of Science and Scopus, then the resolved references are biased toward youth, and a |
| 592 | −constant true age distribution would appear to become younger as the resolvable share rises. The reference |
623 | +constant true age distribution would appear to become younger as the resolvable share rises. |
| 593 | −coverage table of the methodology (declared, internal and external references by year) is the control for |
624 | +Table~\ref{tab:reference_coverage} is the control. The resolved share is nearly constant from 2018 to 2024, |
| 594 | −this and is part of the pending v2 graph; the age shift is reported here as observed, not as corrected. |
625 | +so over those years a resolution bias toward recent works would shift the level of the age distribution but |
| |
626 | +not its trend; the fall of the mean and of the over-ten-year share between 2018 and 2024 is therefore not an |
| |
627 | +artefact of a rising resolvable share. The 2025 and 2026 rows are different: their resolved share is higher |
| |
628 | +and their reference lists shorter (right-truncation), and the small further decline of the mean age in those |
| |
629 | +two rows should not be read on its own. The age shift is reported here as observed within the resolved |
| |
630 | +references, not as corrected for the composition of the unresolved ones, which cannot be typed. |
| 595 | |
631 | |
| 596 | \begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_cited_age}\endgroup |
632 | \begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_cited_age}\endgroup |
| 597 | |
633 | |
| 668 | |
704 | |
| 669 | H4 (convergence) is not testable in its stated form, which concerns citation flows between areas of the |
705 | H4 (convergence) is not testable in its stated form, which concerns citation flows between areas of the |
| 670 | ontology and the modularity of the area network; those statistics await the classification. Its field-level |
706 | ontology and the modularity of the area network; those statistics await the classification. Its field-level |
| 671 | −counterpart, the share of computer-science references that cross into other OpenAlex fields, is flat over the |
707 | +counterpart, the share of computer-science references that cross into other OpenAlex fields, falls through |
| 672 | −window on the v1 graph (Section~\ref{sec:net-flows-fields}), which neither supports nor contradicts the |
708 | +the window with no change of pace at the boundary (Table~\ref{tab:field_flows}, |
| 673 | −within-field convergence the hypothesis describes. |
709 | +Section~\ref{sec:net-flows-fields}), part of the fall being a mechanical consequence of the corpus |
| |
710 | +boundary; it neither supports nor contradicts the within-field convergence the hypothesis describes. |
| 674 | |
711 | |
| 675 | H5 (concentration) has two components. The citation-inequality component is stated for AI categories and is |
712 | H5 (concentration) has two components. The citation-inequality component is stated for AI categories and is |
| 676 | pending; its aggregate counterpart gives a Gini of three-year citations that falls through the baseline and |
713 | pending; its aggregate counterpart gives a Gini of three-year citations that falls through the baseline and |