The cosine series and regular variation in the Karamata and Zygmund senses
Why this work is in the frame
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Bibliographic record
Abstract
The asymptotic behaviour of the coefficients of cosine series is related to the behaviour at the origin of its sum function, in terms of slowly varying functions (SVF’s), and regularly varying sequences. Our work is motivated by the study of the sine series with monotone coefficients of Aljančić, Bojanić and Tomić (1956), which is in terms of SVF’s in the Karamata sense. The direction of our approach to the cosine series is motivated by the recent presentation (using SVF’s in the Zygmund sense) of Samorodnitsky (2016). An obituary for the first author by the second author, with specific relevance to our subject matter, is attached as Section 7.
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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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.000 | 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 it