Bibliographic record
Abstract
Given an $n\times n$ symmetric matrix $W\in [0,1]^{[n]\times [n]}$, let $\mathcal{G}(n,W)$ be the random graph obtained by independently including each edge $jk$ with probability $W_{jk}$. Given a degree sequence ${\bf d}=(d_1,\ldots, d_n)$, let $\mathcal{G}(n,{\bf d})$ denote a uniformly random graph with degree sequence ${\bf d}$. We couple $\mathcal{G}(n,W)$ and $\mathcal{G}(n,{\bf d})$ together so that a.a.s. $\mathcal{G}(n,W)$ is a subgraph of $\mathcal{G}(n,{\bf d})$, where $W$ is some function of ${\bf d}$. Let $Δ({\bf d})$ denote the maximum degree in ${\bf d}$. Our coupling result is optimal when $Δ({\bf d})^2\ll \|{\bf d}\|_1$, i.e.\ $W_{ij}$ is asymptotic to $\mathbb{P}(ij\in \mathcal{G}(n,{\bf d}))$ for every $i,j\in [n]$. We also have coupling results for ${\bf d}$ that are not constrained by the condition $Δ({\bf d})^2\ll \|{\bf d}\|_1$. For such ${\bf d}$ our coupling result is still close to optimal, in the sense that $W_{ij}$ is asymptotic to $\mathbb{P}(ij\in \mathcal{G}(n,{\bf d}))$ for most pairs $i,j\in [n]$.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.034 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.013 |
| Open science | 0.005 | 0.006 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".