Bibliographic record
Abstract
Space limitations do not permit an introduction to all areas of characterizations. The interested reader can, however, find good collections of material on several other topics not mentioned here. Several characterizations of the Poisson process are given by Galambos and Kotz [(9)]. Discrete distributions* are discussed in Galambos [(7)] and in several other contributions in the Calgary Proceedings [(5)]. So-called stability theorems*, in which an assumption is modified “slightly” and one investigates the extent of the effect of this change on a characterization theorem, are surveyed by Lukács [(19)]. Among the multivariate cases, we mentioned the normal distribution. Characterizations for other multivariate distributions are not well developed. The only exceptions are the multivariate extreme-value distributions* (See Chap. 5 in Galambos [(8)]) and some multivariate exponential families* (see Chap. 5 in Galambos and Kotz [(9)]). In addition to the above-mentioned books by Lukács and Laha [(20)], Kagan et al. [(13)], Mathai and Pederzoli [(21)], Galambos [(8)], and Galambos and Kotz [(9)], the reader can find a large variety of results in the Calgary Proceedings [(5)]. Furthermore, a detailed survey of the literature is given by Kotz [(16)] as a supplement to Kagan et al. [(13)]. See also the four-volume set by Johnson and Kotz [(12)], where descriptions of distributions often contain characterization theorems. One of the basic tools of characterizations is the solution of functional equations*. The book by Aczél [(1)] is a useful reference for such results.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.009 | 0.000 |
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 teacher head, 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".