Bibliographic record
Abstract
Abstract Let $$\alpha _1, \ldots , \alpha _m$$ α 1 , … , α m be two or more positive reals with sum 1, let $$C\subseteq {\mathbb {R}}^k$$ C ⊆ R k be an open convex set, and $$f: C\rightarrow {\mathbb {R}}^k$$ f : C → R k be a continuous injection with convex image. For each nonempty set $$S\subseteq C$$ S ⊆ C , let $${\mathscr {M}}(S)$$ M ( S ) be the family of quasi-arithmetic means of all m-tuples of vectors in C with respect to f and the weights $$\alpha _1,\ldots ,\alpha _m$$ α 1 , … , α m , that is, the family $$\begin{aligned} {\mathscr {M}}(S)= \left\{ f^{-1}\left( \alpha _1f(x_1)+\cdots +\alpha _mf(x_m)\right) : x_1,\ldots ,x_m \in S \right\} . \end{aligned}$$ M ( S ) = f - 1 α 1 f ( x 1 ) + ⋯ + α m f ( x m ) : x 1 , … , x m ∈ S . We provide a simple necessary and sufficient condition on S for which the infinite iteration $$\bigcup _{n}{\mathscr {M}}^n(S)$$ ⋃ n M n ( S ) is relatively dense in the convex hull of S.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.073 | 0.026 |
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".