Bibliographic record
Abstract
An original definition of the generalized Euler-Mascheroni constants allowed us to prove that their infinite sum converges to the number (1-Ln2) . By considering this number is the Lebesgue measure of a set defined as the difference between the area of the square unit and the area under the curve y=1/x 1≤x≤2 ; we introduced a partition of this set such that each Lebesgue measure of the subsets can be related to values of Riemann zeta function at integers. From this relationship, we proved that the Lambert W function can produce all ζ(s)  values whatever is the parity of s . Finally, by considering that ζ(s)  values allow calculation of the probability, for s  integers chosen in an interval [1,n] n∈N , to be coprime; we proved that Lambert W function can describe prime numbers distribution.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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 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".