Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In this article, we investigate the quantity mq:=minχ≠χ0|L′/L(1,χ)|, as q→∞ over the primes, where L(s,χ) is the Dirichlet L-function attached to a non-principal Dirichlet character modulo q. Our main result shows that mq≪ log log q/ log q. We also compute mq for every odd prime q up to 107. As a consequence we numerically verified that for every prime q, 3≤q≤107, we have c1/q<mq<5/q, with c1=21/200. In particular, this shows that L′(1,χ)≠0 for every non-principal Dirichlet character χ mod q where 3≤q≤107 is prime, answering a question of Gun, Murty and Rath in this range. We also provide some statistics and scatter plots regarding the mq-values. The programs used and the computational results described here are available at the following web address: https://www.math.unipd.it/~languasc/smallvalues.html.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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