WP44: Appendices B, C (Agent L); Part IV aligned with code; provenance macros

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Simon-Pierre Boucher committed 3 h ago (Nov 3, 2026) parent 3951030 Browse files

11 changed files +950 −14

modified agents/REGISTER.md +1 −1

				`@@ -10,4 +10,4 @@`
10	\| 2026-11-03 \| N (code auditor, subagent) \| prompt in session \| reports/audit/CODE_AUDIT_2026-11-03.md, code_issues.csv (67 issues: 2 blocking, 20 major, 45 minor) \| A: P0 + main P1 fixed in commit of 2026-11-03 17:10 (see reports/DISCREPANCIES_PLAN_VS_CODE.md) \| delivered \|	10	\| 2026-11-03 \| N (code auditor, subagent) \| prompt in session \| reports/audit/CODE_AUDIT_2026-11-03.md, code_issues.csv (67 issues: 2 blocking, 20 major, 45 minor) \| A: P0 + main P1 fixed in commit of 2026-11-03 17:10 (see reports/DISCREPANCIES_PLAN_VS_CODE.md) \| delivered \|
11	\| 2026-11-03 \| L (appendices A/E/H, subagent) \| agents/briefs/WRITER_APPENDICES_AEH.md \| manuscript/appendices/appA_taxonomy.tex (8,360 w), appE_data_dictionary.tex (5,598 w, schema-checked), appH_reproducibility.tex (3,446 w) \| M (compile) + N (Phase 8) \| delivered \|	11	\| 2026-11-03 \| L (appendices A/E/H, subagent) \| agents/briefs/WRITER_APPENDICES_AEH.md \| manuscript/appendices/appA_taxonomy.tex (8,360 w), appE_data_dictionary.tex (5,598 w, schema-checked), appH_reproducibility.tex (3,446 w) \| M (compile) + N (Phase 8) \| delivered \|
12	\| 2026-11-03 \| L (Part II, subagent) \| agents/briefs/WRITER_PART02.md \| manuscript/sections/part02_evolution.tex (12,677 w, 224 verified refs) \| K + M \| delivered \|	12	\| 2026-11-03 \| L (Part II, subagent) \| agents/briefs/WRITER_PART02.md \| manuscript/sections/part02_evolution.tex (12,677 w, 224 verified refs) \| K + M \| delivered \|
13	−\| 2026-11-03 \| L (appendices B/C, subagent) \| agents/briefs/WRITER_APPENDICES_BC.md \| appB_search_and_sources.tex, appC_derivations.tex \| K + M \| running \|	13	+\| 2026-11-03 \| L (appendices B/C, subagent) \| agents/briefs/WRITER_APPENDICES_BC.md \| appB_search_and_sources.tex (5,336 w), appC_derivations.tex (6,509 w), references_appBC.bib (5 verified) \| K + M; A aligned Part IV with the code (α MASI, standardised features, cutoffs, diversity script) \| delivered \|

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modified manuscript/appendices/appB_search_and_sources.tex +2 −2

				`@@ -177,7 +177,7 @@ exists in the slim table of all works but not in the retained subset, that is,`
177	works indexed by DBLP that OpenAlex labels with no computer-science topic.	177	works indexed by DBLP that OpenAlex labels with no computer-science topic.
178	Rather than accept OpenAlex's boundary, the pipeline reads the bucket a	178	Rather than accept OpenAlex's boundary, the pipeline reads the bucket a
179	second time in \emph{identifier-set mode}. The linkage script writes	179	second time in \emph{identifier-set mode}. The linkage script writes
180	−the list \texttt{data/metadata/needed\_oa\_ids.csv} of OpenAlex identifiers to	180	+the list \texttt{data/metadata/}\allowbreak\texttt{needed\_oa\_ids.csv} of OpenAlex identifiers to
181	recover (\LinkNeededOaIdsSecondPassDblpDoi{} reached through a DBLP DOI and	181	recover (\LinkNeededOaIdsSecondPassDblpDoi{} reached through a DBLP DOI and
182	\LinkNeededOaIdsSecondPassArxivDoi{} through an arXiv DOI), and	182	\LinkNeededOaIdsSecondPassArxivDoi{} through an arXiv DOI), and
183	\texttt{openalex\_snapshot.py --id-list} streams every part file again,	183	\texttt{openalex\_snapshot.py --id-list} streams every part file again,
				`@@ -590,7 +590,7 @@ interim figure until the principal investigator's review (checkpoint H-1).`
590		590
591	The acquisition can be repeated from the runbook in six commands, in the	591	The acquisition can be repeated from the runbook in six commands, in the
592	order of Table~\ref{tab:appB-acq}, on a machine with Python~3.12 and the	592	order of Table~\ref{tab:appB-acq}, on a machine with Python~3.12 and the
593	−locked environment of \texttt{reproducibility/environment\_M3U96b.txt}:	593	+locked environment of \texttt{reproducibility/}\allowbreak\texttt{environment\_M3U96b.txt}:
594	\begin{enumerate}	594	\begin{enumerate}
595	\item \texttt{openalex\_snapshot.py} with the manifest copy (then once more with \texttt{--id-list});	595	\item \texttt{openalex\_snapshot.py} with the manifest copy (then once more with \texttt{--id-list});
596	\item \texttt{openalex\_entities.py};	596	\item \texttt{openalex\_entities.py};

modified manuscript/appendices/appC_derivations.tex +376 −1

+ predictive likelihood of $y_{t+1}$. Then $\sum_{r \ge 1}\tilde R_{t+1}(r) =
+ (1-H) Z_t$ and $\tilde R_{t+1}(0) = H Z_t$, so the normaliser is $Z_t$ and
+ \begin{equation}
++  R_{t+1}(0) \;=\; \frac{H Z_t}{H Z_t + (1-H) Z_t} \;=\; H \qquad \text{for every } t.
+   \label{eq:appC-r0}
+ \end{equation}
+ The filtered probability that a changepoint occurs \emph{at} the current
+ backward pass and answers the retrospective question that the offline
+ methods of Sections~\ref{sec:appC-bp} and~\ref{sec:appC-pelt} already
+ address.
++
++\subsection{The Gini coefficient: rank form and Lorenz form}
++\label{sec:appC-gini}
++
++Let $c_{(1)} \le c_{(2)} \le \dots \le c_{(n)}$ be the citation counts of
++the $n$ works of a publication year sorted in ascending order, $S =
++\sum_i c_{(i)} > 0$ their total, and $L_i = \sum_{j \le i} c_{(j)} / S$ the
++cumulative share held by the $i$ least-cited works, with $L_0 = 0$ and
++$L_n = 1$. The Lorenz curve \citep{lorenz1905concentration} is the polygon
++through the points $(i/n, L_i)$, and the Gini coefficient is defined as one
++minus twice the area $A$ under it \citep{ceriani2012gini}. By the
++trapezoidal rule, which is exact for a polygon,
++\begin{equation}
++  A \;=\; \sum_{i=1}^{n} \frac{1}{n}\cdot\frac{L_{i-1} + L_i}{2}
++    \;=\; \frac{1}{2n}\Bigl( 2\sum_{i=1}^{n} L_i - L_n \Bigr)
++    \;=\; \frac{1}{n}\sum_{i=1}^{n} L_i - \frac{1}{2n}.
++\end{equation}
++Exchanging the order of summation in $\sum_i L_i$,
++\begin{equation}
++  \sum_{i=1}^{n} L_i \;=\; \frac{1}{S}\sum_{i=1}^{n}\sum_{j=1}^{i} c_{(j)}
++    \;=\; \frac{1}{S}\sum_{j=1}^{n} (n - j + 1)\, c_{(j)}
++    \;=\; (n+1) - \frac{1}{S}\sum_{j=1}^{n} j\, c_{(j)},
++\end{equation}
++so that
++\begin{equation}
++  G \;=\; 1 - 2A
++    \;=\; 1 - \frac{2(n+1)}{n} + \frac{2}{nS}\sum_{j=1}^{n} j\, c_{(j)} + \frac{1}{n}
++    \;=\; \frac{2\sum_{j=1}^{n} j\, c_{(j)}}{n \sum_{j} c_{(j)}} - \frac{n+1}{n},
++  \label{eq:appC-gini}
++\end{equation}
++which is equation~\eqref{eq:gini} of Part~IV and the expression that
++\texttt{bibliometrics/03\_citation\_impact.py} evaluates in SQL, the rank
++$j$ being the window function \texttt{row\_number()} partitioned by year and
++ordered by the citation count and then by the work identifier.
++The secondary ordering by work identifier is needed only to make the rank a
++permutation when counts tie; since tied values receive consecutive ranks and
++contribute $c \cdot (j + j')$ to the numerator whichever of the two tied
++works gets the smaller rank, the value of $G$ does not depend on how ties are
++broken. The bounds follow from \eqref{eq:appC-gini}: $G = 0$ when all
++$c_{(j)}$ are equal (then $\sum_j j c_{(j)} = c\,n(n+1)/2$ and the two terms
++cancel), and $G = 1 - 1/n$ when a single work holds all citations (then
++$\sum_j j c_{(j)} = nS$), so the maximum attainable value is $1 - 1/n$ rather
++than one and the coefficient is not normalised by that factor. Uncited works
++enter with $c_{(j)} = 0$ at the lowest ranks; adding $u$ uncited works to a
++year leaves $\sum_j j c_{(j)}$ shifted by $uS$ and $n$ increased by $u$, and
++one checks from \eqref{eq:appC-gini} that $G$ increases, which is the
++direction stated in Part~IV and the reason the uncited share accompanies the
++coefficient in the tables.
++
++\subsection{Rao--Stirling and Leinster--Cobbold at order two}
++\label{sec:appC-diversity}
++
++Let $p \in \R^K$ be a probability vector over categories, $\delta_{ij} \in
++[0,1]$ a dissimilarity with $\delta_{ii} = 0$, and $Z = (z_{ij})$ the
++similarity matrix $z_{ij} = 1 - \delta_{ij}$, so that $z_{ii} = 1$. The
++Rao--Stirling index \citep{rao1982diversity, stirling2007diversity} is
++$\Delta_{\mathrm{RS}}(p) = \sum_{i \ne j} p_i p_j \delta_{ij} = p^{\top}\Delta p$
++with $\Delta = (\delta_{ij})$, the diagonal contributing nothing. The
++Leinster--Cobbold diversity of order $q$ \citep{leinster2012diversity} is
++${}^{q}D^{Z}(p) = \bigl(\sum_{i : p_i > 0} p_i (Zp)_i^{q-1}\bigr)^{1/(1-q)}$;
++at $q = 2$ the exponent $1/(1-q) = -1$ and the inner power is one, so
++\begin{equation}
++  {}^{2}D^{Z}(p) \;=\; \Bigl(\sum_i p_i (Zp)_i\Bigr)^{-1} \;=\; \frac{1}{p^{\top} Z p}.
++\end{equation}
++Since $Z = \mathbf{1}\mathbf{1}^{\top} - \Delta$ entrywise (using $z_{ii} = 1
++= 1 - \delta_{ii}$ on the diagonal as well), and $p^{\top}\mathbf{1}\mathbf{1}^{\top}p
++= (\sum_i p_i)^2 = 1$,
++\begin{equation}
++  p^{\top} Z p \;=\; 1 - p^{\top}\Delta p \;=\; 1 - \Delta_{\mathrm{RS}}(p),
++  \qquad\text{hence}\qquad
++  {}^{2}D^{Z}(p) \;=\; \frac{1}{1 - \Delta_{\mathrm{RS}}(p)},
++  \label{eq:appC-lc2}
++\end{equation}
++the identity quoted in Part~IV\@. It shows that at order two the two
++families carry the same information: ${}^{2}D^{Z}$ is a strictly increasing
++function of $\Delta_{\mathrm{RS}}$ on $[0, 1)$, and the ordering of years or
++categories by either index is the same. They differ in scale and in
++behaviour near saturation. $\Delta_{\mathrm{RS}}$ is bounded by the mean
++dissimilarity and compresses differences among very even distributions;
++${}^{2}D^{Z}$ is an effective number of categories, equal to $K$ for the
++uniform distribution over $K$ mutually dissimilar categories
++($\Delta_{\mathrm{RS}} = 1 - 1/K$) and to one for a distribution concentrated
++on a single category ($\Delta_{\mathrm{RS}} = 0$), and it expands the
++compressed end. The identity requires only $z_{ii} = 1$ and $z_{ij} = 1 -
++\delta_{ij}$; it does not require $\delta$ to be a metric, and the
++dissimilarity used, one minus a cosine similarity of category centroids,
++is not one. The script \texttt{bibliometrics/04\_diversity\_cagr.py}
++computes both quantities from the yearly category mix exactly as
++\eqref{eq:appC-lc2} prescribes, $\Delta_{\mathrm{RS}} = p^{\top}(1 - Z)p$
++with the diagonal of $Z$ set to one and ${}^{2}D^{Z} = 1/(p^{\top}Zp)$, and
++attaches a percentile bootstrap interval to $\Delta_{\mathrm{RS}}$ by
++multinomial resampling of the works over categories ($B = 500$, seed 44),
++which is the sampling model under which the category counts of a year are
++a multinomial draw of fixed size; the interval of ${}^{2}D^{Z}$ follows by
++the monotone transformation.
++
++\subsection{Modularity of a directed weighted graph at a fixed partition}
++\label{sec:appC-modularity}
++
++Let $W \in \R_{\ge 0}^{K \times K}$ be the flow matrix of a citing year,
++$W_{ij}$ the number of citations from category $i$ to category $j$, with
++$m = \sum_{ij} W_{ij}$, out-strength $k^{\mathrm{out}}_i = \sum_j W_{ij}$ and
++in-strength $k^{\mathrm{in}}_j = \sum_i W_{ij}$, and let $g : \{1, \dots, K\}
++\to \mathcal{G}$ be a given assignment of categories to communities. The
++statistic implemented by \texttt{modularity()} in
++\texttt{knowledge\_graph/02\_category\_flows.py} is
++\begin{equation}
++  Q(W, g) \;=\; \frac{1}{m}\sum_{i,j}\Bigl( W_{ij} - \frac{k^{\mathrm{out}}_i k^{\mathrm{in}}_j}{m} \Bigr)\mathbf{1}[g_i = g_j],
++  \label{eq:appC-Q}
++\end{equation}
++the directed form of \citet{leicht2008directed}, which reduces to the
++Newman--Girvan modularity \citep{newman2004community} when $W$ is symmetric
++(then $k^{\mathrm{out}} = k^{\mathrm{in}} = k$ and $m = 2|E|$ for an
++unweighted graph). Three facts are used in Part~IV\@. First, the null term
++is the expected weight of the edge $i \to j$ under random rewiring that
++preserves every node's out- and in-strength in expectation: a configuration
++model in which each of the $m$ units of weight leaves node $i$ with
++probability $k^{\mathrm{out}}_i/m$ and enters node $j$ with probability
++$k^{\mathrm{in}}_j/m$ independently gives expected weight
++$m \cdot (k^{\mathrm{out}}_i/m)(k^{\mathrm{in}}_j/m) = k^{\mathrm{out}}_i
++k^{\mathrm{in}}_j/m$, and summing over $j$ recovers $k^{\mathrm{out}}_i$, so
++the null model has the observed strengths. Second, $Q$ vanishes when all
++nodes are in one community: then the indicator is identically one and
++$\sum_{ij} W_{ij} = m = \sum_{ij} k^{\mathrm{out}}_i k^{\mathrm{in}}_j/m$.
++Third, writing $e_{gg} = \sum_{i,j : g_i = g_j = g} W_{ij}/m$ for the fraction
++of weight inside community $g$, $a^{\mathrm{out}}_g = \sum_{i : g_i = g}
++k^{\mathrm{out}}_i/m$ and $a^{\mathrm{in}}_g$ likewise,
++\begin{equation}
++  Q \;=\; \sum_{g \in \mathcal{G}} \bigl( e_{gg} - a^{\mathrm{out}}_g\, a^{\mathrm{in}}_g \bigr),
++  \label{eq:appC-Qcomm}
++\end{equation}
++so that $Q \le \sum_g e_{gg} \le 1$ and $Q \ge -\sum_g a^{\mathrm{out}}_g
++a^{\mathrm{in}}_g \ge -1$; the value is positive when more weight stays
++inside communities than the strength-preserving null predicts. The
++self-share reported alongside, $\operatorname{tr}(W)/m = \sum_i e_{ii}$ at
++the category partition, is the first term of \eqref{eq:appC-Qcomm} alone and
++differs from $Q_{\mathrm{cat}}$ by the correction $\sum_i a^{\mathrm{out}}_i
++a^{\mathrm{in}}_i$, which grows with the concentration of flows on a few
++large categories. For the area partition, \eqref{eq:appC-Qcomm} is summed
++over the eight areas with $e_{\alpha\alpha}$ the within-area share, which is
++one minus the cross-area share $X_{\alpha,t}$ of Part~IV weighted by the
++area's out-strength; $Q_{\mathrm{area}}$ is therefore a strength-weighted,
++null-corrected average of the within-area shares, and a fall in
++$Q_{\mathrm{area}}$ can arise from a rise in boundary crossing or from a
++shift of out-strength toward areas whose $a^{\mathrm{out}}_\alpha
++a^{\mathrm{in}}_\alpha$ is large. Because the partition is fixed rather than
++optimised, none of the resolution-limit results for maximised modularity
++\citep{fortunato2007resolution} applies; $Q$ is here a descriptive index and
++its comparison across years is meaningful only because the partition and
++the category definitions are the same in every year.
++
++\subsection{Krippendorff's \texorpdfstring{$\alpha$}{alpha} with the MASI distance}
++\label{sec:appC-alpha}
++
++\paragraph{General form.}
++Krippendorff's $\alpha$ \citep{hayes2007krippendorff, artstein2008agreement}
++is defined for any difference function $d(v, v') \ge 0$ on the values that
++coders may assign, with $d(v, v) = 0$, as
++\begin{equation}
++  \alpha \;=\; 1 - \frac{D_o}{D_e},
++  \label{eq:appC-alpha}
++\end{equation}
++where $D_o$ is the mean difference between the values assigned to the same
++unit by different coders and $D_e$ the mean difference between all pairs of
++values in the pooled data, irrespective of unit. With two coders $A$ and $B$
++rating each of $n$ units, the pooled set contains $N = 2n$ values and
++\begin{equation}
++  D_o \;=\; \frac{1}{n}\sum_{u=1}^{n} d\bigl(a_u, b_u\bigr), \qquad
++  D_e \;=\; \frac{1}{N(N-1)}\sum_{c \ne c'} d\bigl(v_c, v_{c'}\bigr)
++        \;=\; \frac{1}{\binom{N}{2}}\sum_{c < c'} d\bigl(v_c, v_{c'}\bigr),
++  \label{eq:appC-DoDe}
++\end{equation}
++the second equality using the symmetry of $d$. The coefficient is one when
++the coders agree on every unit ($D_o = 0$), zero when the within-unit
++differences are what chance pairing of the pooled values would produce
++($D_o = D_e$), and negative when disagreement is systematic. Unlike Cohen's
++$\kappa$, which compares observed agreement with the product of the two
++coders' marginals, $\alpha$ pools the two coders' values into one
++distribution for its chance term, so it does not reward coders for having
++different marginal distributions; this and its accommodation of arbitrary
++difference functions are the reasons it is the recommended coefficient for
++set-valued annotation \citep{artstein2008agreement}.
++
++\paragraph{The MASI distance.}
++For set-valued labels $x, y \subseteq \mathcal{K}$, \citet{passonneau2006masi}
++defines the Measuring Agreement on Set-valued Items distance as
++\begin{gather}
++  d_{\mathrm{MASI}}(x, y) \;=\; 1 - J(x, y)\, M(x, y), \qquad
++  J(x, y) = \frac{|x \cap y|}{|x \cup y|}, \nonumber\\
++  M(x, y) =
++  \begin{cases}
++    1    & x = y,\\
++    2/3  & x \subsetneq y \text{ or } y \subsetneq x,\\
++    1/3  & x \cap y \ne \emptyset \text{ and neither contains the other},\\
++    0    & x \cap y = \emptyset ,
++  \end{cases}
++  \label{eq:appC-masi}
++\end{gather}
++the Jaccard similarity attenuated by a monotonicity factor that
++distinguishes nesting from mere overlap. The distance is zero only for
++identical non-empty sets, equals one for disjoint sets, and treats the pair
++(empty, empty) as identical ($d = 0$) by the convention of the
++implementation, which returns zero before computing $J$ for two empty sets;
++the pair (empty, non-empty) has $J = 0$ and $d = 1$.
++
++\paragraph{What the code computes.}
++\texttt{taxonomy/validate\_sample.py} forms, for the two raters, the
++observed term as the mean of $d_{\mathrm{MASI}}^2$ over the $n$ rated works
++and the expected term as the mean of $d_{\mathrm{MASI}}^2$ over all
++unordered pairs of the $2n$ pooled label sets (exhaustively when
++$2n \le 1200$, otherwise over 200{,}000 random ordered pairs with $i \ne j$,
++seed 44), and reports $1 - D_o/D_e$. Two remarks make this precise. The code
++uses the constants $0.67$ and $0.33$ for the monotonicity factor rather than
++$2/3$ and $1/3$, a rounding of the published definition that changes
++distances by at most $0.0034$. More consequentially, it \emph{squares} the
++MASI distance before averaging, that is, it applies
++\eqref{eq:appC-alpha}--\eqref{eq:appC-DoDe} with $d = d_{\mathrm{MASI}}^2$.
++Krippendorff's interval metric is the squared difference, and the code's
++comment describes the computation as the ``interval form on the MASI
++distance''; \citeauthor{passonneau2006masi}, in contrast, plugs
++$d_{\mathrm{MASI}}$ itself into the $\alpha$ formula, and the agreement
++packages that implement MASI follow her. The two conventions yield different
++numbers from the same ratings---squaring compresses small disagreements and
++so, as a rule, raises $\alpha$ when most disagreements are partial---and the
++value reported in Part~IX is the squared-distance version, labelled as such.
++Both are legitimate instances of \eqref{eq:appC-alpha}; what is not
++legitimate is to compare the reported value with published MASI-$\alpha$
++figures without this caveat. The mean Jaccard index reported next to it is
++$n^{-1}\sum_u J(a_u, b_u)$ with $0/0 = 0$ and is a raw agreement rate with
++no chance correction. Both statistics are computed on the full rated sample
++and not on the 200-work subsample reserved for the principal investigator,
++whose verdicts will add a third coder to \eqref{eq:appC-DoDe} once
++checkpoint H-2 is signed.
++
++\subsection{The multi-label score rule and the tie-break as a total order}
++\label{sec:appC-score}
++
++\paragraph{Score.}
++For a work $w$ and a category $k$ the implementation
++(\texttt{taxonomy/classify.py}, \texttt{score\_row}) computes five
++components, one per signal type $\sigma \in \{\mathrm{T}, \mathrm{F},
++\mathrm{X}, \mathrm{D}, \mathrm{kw}\}$,
++\begin{align}
++  s^{\sigma}_k(w) &\;=\; \min\Bigl\{ 1,\ \sum_{x \in \sigma(w)} \omega^{\sigma}_k(x) \Bigr\}
++  \qquad (\sigma \ne \mathrm{kw}), \\
++  s^{\mathrm{kw}}_k(w) &\;=\; \min\Bigl\{ 1,\ \sum_{(r, \omega, \phi) \in R_k} \omega\, \mathbf{1}[r \text{ matches } \phi(w)] \Bigr\},
++\end{align}
++where $\sigma(w)$ is the \emph{set} of the work's topic, subfield, arXiv
++category or DBLP stream identifiers (Python \texttt{set()}, so a repeated
++identifier contributes once), and the keyword loop stops at the first rule
++that brings the running sum to one, which is equivalent to the capped sum.
++The score is $s_k(w) = \sum_\sigma s^{\sigma}_k(w) \in [0, 5]$; a category
++with $s_k(w) \ge \theta = 1$ is then vetoed if any exclusion pattern of
++$Z_k$ matches the concatenation of title and abstract, in which case its
++score is set to zero and it is not assigned. The set of assigned categories
++is $C(w) = \{k : s_k(w) \ge \theta,\ \text{not vetoed}\}$, and the stored
++score of an assigned category is $s_k(w)$ rounded to three decimals. Two
++elementary properties justify the reading given in Part~IV\@. The cap makes
++each component a bounded, monotone, subadditive function of the matched
++weights: adding a signal never lowers a component, and no number of signals
++of one type can contribute more than one. And because the threshold equals
++the cap, a single weight-one signal of any type suffices for assignment
++while signals of weight below one require corroboration from a different
++type; formally, $s_k(w) \ge 1$ holds if and only if either some component
++reaches one or the sum of the (uncapped) components across at least two
++types reaches one.
++
++\paragraph{Primary category as the minimum of a total order.}
++Let $\mathcal{P}(w) = \bigcup_{k \in C(w)} \mathrm{parents}(k)$ be the set
++of categories declared parents of at least one assigned category (the
++\texttt{child\_of} relation of the ontology). The implementation sorts the
++assigned categories by the key
++\begin{equation}
++  \phi(k) \;=\; \bigl( -s_k(w),\ \mathbf{1}[k \in \mathcal{P}(w)],\ \mathrm{number}(k) \bigr) \in \R \times \{0,1\} \times \mathbb{N}
++  \label{eq:appC-key}
++\end{equation}
++in lexicographic order and takes the first element; this is
++$\kappa^{\ast}(w) = \arg\min_{k \in C(w)} \phi(k)$ and coincides with the
++lexicographic arg-max of Part~IV (the sign of the first component reversed).
++The lexicographic order on $\R \times \{0,1\} \times \mathbb{N}$ is a total
++order, and $\phi$ is injective on $\mathcal{K}$ because the ontology numbers
++are distinct, so the restriction of $\phi$ to $C(w)$ has a unique minimum
++whenever $C(w) \ne \emptyset$: the primary category is well defined and does
++not depend on the order in which categories are scanned. The second
++component implements ``child before parent'': if $k$ and $k'$ are both
++assigned with equal scores and $k'$ is a declared parent of $k$, then
++$k' \in \mathcal{P}(w)$ while $k$ may not be, and $k$ precedes $k'$. The rule
++is not transitive in the sense of a hierarchy, however. Membership in
++$\mathcal{P}(w)$ depends only on whether $k$ is the parent of \emph{some}
++assigned category, not of the specific competitor; a category that is the
++parent of a low-scoring assigned child is demoted in the tie against an
++unrelated category of equal score. This is a property of the key as
++implemented, stated here so that the primary counts of Part~IX are read with
++it; it affects only exact ties in a score rounded to three decimals, which
++are frequent precisely among the categories whose signals are weight-one
++keywords. The third component, the ontology number, is arbitrary and makes
++the order total; no claim is attached to it.
++
++\subsection{The emerging-topic label and the absence of look-ahead}
++\label{sec:appC-lookahead}
++
++\paragraph{Filtrations.}
++Index months by integers $t = 0, 1, \dots, M$ (January 2018 to the last
++complete month) and let the panel of \texttt{experiments/emerging\_detection.py}
++be the pair of arrays $n_{k,t}$ (eligible month-precision works of topic $k$
++with first month $t$) and $c_{k,t}$ (internal citations received by works of
++topic $k$ from works with first month $t$). Define the filtration
++\begin{equation}
++  \mathcal{F}_T \;=\; \sigma\bigl( n_{k,t},\ c_{k,t} :\ k \in \mathcal{K}_{\mathrm{top}},\ t \le T \bigr),
++  \label{eq:appC-filtration}
++\end{equation}
++the information contained in the panel columns up to and including month
++$T$. A statistic is \emph{available at} $T$ if it is
++$\mathcal{F}_T$-measurable. Each of the six features of Part~IV is a
++function of sums of panel entries over windows $(a, b]$ with $b \le T$:
++$g^{12}_{k,T}$ uses $(T-24, T]$, $\mathrm{acc}_{k,T}$ uses $(T-36, T]$,
++$z_{k,T}$ uses $[T-27, T]$, $\mathrm{cit}_{k,T}$ uses $(T-24, T]$ of $c$,
++$\mathrm{share}_{k,T}$ uses $(T-12, T]$ of every topic, and
++$\mathrm{age}_{k,T}$ uses the cumulative sum up to $T$. All are
++$\mathcal{F}_T$-measurable by construction. The implementation enforces this
++by index arithmetic (\texttt{win(a, lo, hi)} slices columns \texttt{lo+1}
++to \texttt{hi} inclusive with \texttt{hi = T\_idx}), not by convention.
++
++\paragraph{Label.}
++The label $\ell_{k,T,h}$ of equation~\eqref{eq:label} is a function of
++$V_k(T-h, T]$, $V_k(T, T+h]$, $V_k(T-12, T]$ and of the within-cutoff decile
++of $g^{\mathrm{fut}}$ over eligible topics; it is therefore
++$\mathcal{F}_{T+h}$-measurable and, because it depends on columns strictly
++after $T$, not $\mathcal{F}_T$-measurable. The feature--label pair at cutoff
++$T$ thus has the structure of a prediction problem: predict an
++$\mathcal{F}_{T+h}$-measurable outcome from an $\mathcal{F}_T$-measurable
++input. The eligibility condition $V_k(T-12, T] \ge 20$ is
++$\mathcal{F}_T$-measurable, so conditioning on it does not leak the outcome.
++
++\paragraph{Separation of training and test.}
++Let $\mathcal{T}_{\mathrm{tr}}$ and $\mathcal{T}_{\mathrm{te}}$ be the
++training and test cutoffs. Every quantity used to fit a model---features,
++labels and the standardisation constants of the scaler, which is fitted on
++training rows only---is $\mathcal{F}_{T^{\mathrm{tr}}_{\max} + h}$-measurable
++with $T^{\mathrm{tr}}_{\max} = \max \mathcal{T}_{\mathrm{tr}}$. The
++implementation sets $T^{\mathrm{tr}}_{\max}$ to December 2021 for $h = 12$
++and to December 2020 for $h = 24$, so that $T^{\mathrm{tr}}_{\max} + h$ is
++December 2022 in both cases, and the first test cutoff is January 2023.
++Hence
++\begin{equation}
++  T^{\mathrm{tr}}_{\max} + h \;<\; \min \mathcal{T}_{\mathrm{te}},
++  \label{eq:appC-gap}
++\end{equation}
++and the fitted predictor is measurable with respect to a $\sigma$-field
++that precedes every test feature, let alone every test label, which closes
++at $\max \mathcal{T}_{\mathrm{te}} + h \le M$. Condition \eqref{eq:appC-gap}
++is the formal content of ``out of time'' in the sense of
++\citet{bergmeir2012crossval}; it is stricter than the plan's wording, which
++allowed training cutoffs through 2022, and stricter for $h = 24$ than the
++description of Part~IV, which gives December 2021 as the last training
++cutoff for both horizons---the code's rule is the one that guarantees
++\eqref{eq:appC-gap}, and the manuscript follows the code. The test cutoffs
++are further restricted to those with $T + h \le M$, so that no test label is
++right-censored.
++
++\paragraph{What measurability does not cover.}
++The filtration \eqref{eq:appC-filtration} is generated by the panel, and the
++panel is built once, in 2026, from a corpus whose topic assignments,
++eligibility flags, linkage and month-precision filter were all fixed with
++knowledge of the whole period. Formally, the random objects $n_{k,t}$
++themselves are not $\mathcal{F}_t$-measurable functionals of the literature
++as it stood at $t$: they are functionals of the literature as OpenAlex
++indexed and classified it by October 2026. The statement proved above is
++therefore conditional: \emph{given} the 2026 panel, no feature at $T$ uses a
++column after $T$ and no training quantity uses a column at or after the
++first test cutoff. It is not the statement that an observer in 2021 could
++have computed the training set, which would require a topic vocabulary and a
++corpus frozen in 2021. Part~IV draws the distinction and names the
++cluster-based extension that would narrow it; the derivation here makes
++precise which half of the claim is proved and which is assumed.

modified manuscript/references_appBC.bib +1 −1

				`@@ -4,7 +4,7 @@`
4	% are reused and never redefined here.	4	% are reused and never redefined here.
5		5
6	@article{jackson2005optimal,	6	@article{jackson2005optimal,
7	− author = {Jackson, Brad and Scargle, Jeffrey D. and Barnes, David and Arabhi, Sundararajan and Alt, Alina and Gioumousis, Peter and Gwin, Elyus and Sangtrakulcharoen, Paungkaew and Tan, Linda and Tsai, Tun Tao},	7	+ author = {Jackson, B. and Scargle, J. D. and Barnes, D. and Arabhi, S. and Alt, A. and Gioumousis, P. and Gwin, E. and others},
8	title = {An algorithm for optimal partitioning of data on an interval},	8	title = {An algorithm for optimal partitioning of data on an interval},
9	journal = {IEEE Signal Processing Letters},	9	journal = {IEEE Signal Processing Letters},
10	year = {2005},	10	year = {2005},

modified manuscript/references_verification_appBC.csv +1 −1

				`@@ -1,5 +1,5 @@`
1	key,doi_or_arxiv,verified_via,verified_title,match	1	key,doi_or_arxiv,verified_via,verified_title,match
2	−jackson2005optimal,10.1109/LSP.2001.838216,crossref,An algorithm for optimal partitioning of data on an interval,yes	2	+jackson2005optimal,10.1109/LSP.2001.838216,crossref+openalex W2097880821,An algorithm for optimal partitioning of data on an interval,yes (authors 8-10 given as 'P. San; L. Tan; Tun Tao Tsai' in both records; entry lists the first seven verified names and 'others')
3	lorenz1905concentration,10.1080/15225437.1905.10503443,crossref,Methods of Measuring the Concentration of Wealth,yes	3	lorenz1905concentration,10.1080/15225437.1905.10503443,crossref,Methods of Measuring the Concentration of Wealth,yes
4	passonneau2006masi,10.63317/4nuo6thi27ax,crossref+openalex W1747645360,Measuring Agreement on Set-valued Items (MASI) for Semantic and Pragmatic Annotation,yes	4	passonneau2006masi,10.63317/4nuo6thi27ax,crossref+openalex W1747645360,Measuring Agreement on Set-valued Items (MASI) for Semantic and Pragmatic Annotation,yes
5	artstein2008agreement,10.1162/coli.07-034-R2,crossref,Inter-Coder Agreement for Computational Linguistics,yes	5	artstein2008agreement,10.1162/coli.07-034-R2,crossref,Inter-Coder Agreement for Computational Linguistics,yes

modified manuscript/sections/part04_methodology.tex +17 −8

				`@@ -521,10 +521,11 @@ the works to which rater $r$ assigned primary $k$; $\kappa$ is computed between`
521	the two raters and between the rules and each rater. Agreement on the label	521	the two raters and between the rules and each rater. Agreement on the label
522	sets is measured by the mean Jaccard index	522	sets is measured by the mean Jaccard index
523	$\bar J = n^{-1}\sum_w \|C^{A}(w) \cap C^{B}(w)\| / \|C^{A}(w) \cup C^{B}(w)\|$	523	$\bar J = n^{-1}\sum_w \|C^{A}(w) \cap C^{B}(w)\| / \|C^{A}(w) \cup C^{B}(w)\|$
524	−(with the convention $0/0 = 0$). The validation note announces Krippendorff's	524	+(with the convention $0/0 = 0$), and by Krippendorff's $\alpha$ with the
525	−$\alpha$ with the MASI distance for the multi-label agreement; the metrics	525	+MASI distance of \citet{passonneau2006masi} between the two raters' label
526	−script computes the mean Jaccard index instead, and the manuscript reports	526	+sets, in its interval form ($\alpha = 1 - D_o/D_e$ with squared MASI
527	−what is computed. A work is exported as a disagreement for human review when	527	+distances, $D_o$ the mean observed distance over works and $D_e$ the mean
		528	+distance over all pairs of label sets); the derivation is in Appendix~C. A work is exported as a disagreement for human review when
528	the rules, rater~A and rater~B have no category in common although at least	529	the rules, rater~A and rater~B have no category in common although at least
529	one of them assigned one.	530	one of them assigned one.
530		531
				`@@ -767,7 +768,12 @@ pipeline computes the category flow matrices from which $p$ is formed`
767	(Section~\ref{sec:m-networks}) and the centroid similarities, but the two	768	(Section~\ref{sec:m-networks}) and the centroid similarities, but the two
768	diversity indices are not yet produced by a script; they are defined here	769	diversity indices are not yet produced by a script; they are defined here
769	because the protocol commits to them, and their values in Part IX are	770	because the protocol commits to them, and their values in Part IX are
770	−\pending{Rao--Stirling and Leinster--Cobbold indices per category and period, not yet computed}	771	+The yearly Rao--Stirling and Leinster--Cobbold indices of the category mix,
		772	+with bootstrap intervals from multinomial resampling of works over categories
		773	+($B = 500$, seed 44), are computed by \texttt{bibliometrics/04\_diversity\_cagr.py}
		774	+and reported in Part~IX; the dissimilarity $d_{ij}$ is one minus the cosine
		775	+similarity of category centroids when embeddings are available and one minus
		776	+the co-classification Jaccard similarity otherwise.
771	until the computation is added and audited.	777	until the computation is added and audited.
772		778
773	\section{Citation and collaboration networks}	779	\section{Citation and collaboration networks}
				`@@ -1370,7 +1376,9 @@ positives separately.`
1370		1376
1371	\subsection{Cutoffs, models and metrics}	1377	\subsection{Cutoffs, models and metrics}
1372		1378
1373	−Training cutoffs are every third month from December 2019 to December 2021;	1379	+Training cutoffs are every third month from December 2019 to December 2021
		1380	+for the 12-month horizon and to December 2020 for the 24-month horizon, so
		1381	+that every training label is observable before the first test cutoff;
1374	test cutoffs are every third month from January 2023 to October 2024 for	1382	test cutoffs are every third month from January 2023 to October 2024 for
1375	which $T + h$ lies within the panel. With $h = 24$ the last training label	1383	which $T + h$ lies within the panel. With $h = 24$ the last training label
1376	uses data to December 2023, which is after the reference date but more than a	1384	uses data to December 2023, which is after the reference date but more than a
				`@@ -1385,8 +1393,9 @@ above with non-finite values replaced by zero.`
1385		1393
1386	Three predictors are compared: the $z$-score baseline, which ranks topics by	1394	Three predictors are compared: the $z$-score baseline, which ranks topics by
1387	$z_{k,T}$ alone and involves no fitting; an $\ell_2$-regularised logistic	1395	$z_{k,T}$ alone and involves no fitting; an $\ell_2$-regularised logistic
1388	−regression (regularisation strength $C = 1$, on unstandardised features, so	1396	+regression (regularisation strength $C = 1$, on features standardised with a
1389	−the penalty is not scale-invariant and acts most on the small-range features);	1397	+scaler fitted on the training cutoffs only, so that the penalty is
		1398	+scale-invariant and no test-period statistic enters the fit);
1390	and a gradient boosting classifier \citep{friedman2001gbm} with 300 trees of	1399	and a gradient boosting classifier \citep{friedman2001gbm} with 300 trees of
1391	depth three and learning rate 0.05, seed 44, as implemented in scikit-learn	1400	depth three and learning rate 0.05, seed 44, as implemented in scikit-learn
1392	\citep{pedregosa2011sklearn}. The metrics on the pooled test rows are the area	1401	\citep{pedregosa2011sklearn}. The metrics on the pooled test rows are the area

modified manuscript/tables/numbers.tex +15 −0

+ \newcommand{\LinkSlimTotal}{464{,}765{,}485}
+ \newcommand{\LinkSlimCsAnyTwoZeroOneEightTwoZeroTwoSix}{15{,}490{,}159}
+ \newcommand{\LinkSeconds}{10}
++\newcommand{\DblpParsedRecords}{8{,}840{,}866}
++\newcommand{\DblpTypeIncollection}{71{,}247}
++\newcommand{\DblpTypeBook}{21{,}648}
++\newcommand{\DblpTypeProceedings}{65{,}792}
++\newcommand{\DblpTypeMastersthesis}{27}
++\newcommand{\DblpTypeData}{30{,}631}
++\newcommand{\DblpTypeArticle}{4{,}500{,}501}
++\newcommand{\DblpTypeInproceedings}{3{,}995{,}530}
++\newcommand{\DblpTypePhdthesis}{158{,}398}
++\newcommand{\AclParsedEntries}{138{,}796}
++\newcommand{\IncrementApiCalls}{1{,}002}
++\newcommand{\IncrementRecordsRetrieved}{193{,}369}
++\newcommand{\IncrementTruncatedSlices}{1}
++\newcommand{\IncrementSlicesDone}{64}
++\newcommand{\IncrementCostUsd}{0.100}

modified tables/make_numbers.py +13 −0

				`@@ -43,5 +43,18 @@ for f, key in [("results/econometrics/its_results.json", "its"), ("taxonomy/vali`
43	if os.path.exists(p):	43	if os.path.exists(p):
44	d = json.load(open(p))	44	d = json.load(open(p))
45	walk(key, {k: v for k, v in d.items() if not isinstance(v, (list,))})	45	walk(key, {k: v for k, v in d.items() if not isinstance(v, (list,))})
		46	+for f, key in [("data/metadata/dblp_parse_report.json", "dblp"), ("data/metadata/acl_parse_report.json", "acl"), ("data/metadata/api_increment_ledger.json", "increment"), ("data/metadata/increment_report.json", "incrementIngest")]:
		47	+ p = os.path.join(R, f)
		48	+ if os.path.exists(p):
		49	+ d = json.load(open(p))
		50	+ if key == "increment":
		51	+ sl = d.get("slices", {}); emit("increment api calls", d.get("calls", 0)); emit("increment records retrieved", sum(v.get("records", 0) for v in sl.values()))
		52	+ emit("increment truncated slices", sum(1 for v in sl.values() if v.get("truncated"))); emit("increment slices done", sum(1 for v in sl.values() if v.get("done"))); emit("increment cost usd", round(d.get("cost_usd_total", 0), 4))
		53	+ elif key == "incrementIngest":
		54	+ emit("increment new works", d.get("new_works", 0)); emit("increment already in snapshot", d.get("already_in_snapshot", 0))
		55	+ elif key == "dblp":
		56	+ emit("dblp parsed records", d.get("rows_written", 0)); [emit(f"dblp type {k}", v) for k, v in d.get("counts_by_type", {}).items()]
		57	+ elif key == "acl":
		58	+ emit("acl parsed entries", d.get("entries", 0))
46	open(os.path.join(R, "manuscript/tables/numbers.tex"), "w").write("% machine-generated by tables/make_numbers.py — do not edit\n" + "\n".join(out) + "\n")	59	open(os.path.join(R, "manuscript/tables/numbers.tex"), "w").write("% machine-generated by tables/make_numbers.py — do not edit\n" + "\n".join(out) + "\n")
47	print(len(out), "macros")	60	print(len(out), "macros")
48		61

spb/wp44_uqo

WP44: Appendices B, C (Agent L); Part IV aligned with code; provenance macros

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