Why this work is in the frame
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Bibliographic record
Abstract
Motivated by the classical Frobenius problem, we introduce the Frobenius poset on the integers $\mathbb{Z}$, that is, for a sub-semigroup $\Lambda$ of the non-negative integers $(\mathbb{N},+)$, we define the order by $n \leq_{\Lambda} m$ if $m-n \in \Lambda$. When $\Lambda$ is generated by two relatively prime integers $a$ and $b$, we show that the order complex of an interval in the Frobenius poset is either contractible or homotopy equivalent to a sphere. We also show that when $\Lambda$ is generated by the integers $\{a,a+d,a+2d,\ldots,a+(a-1)d\}$, the order complex is homotopy equivalent to a wedge of spheres. Motivé par le problème de Frobenius classique, nous introduisons l'ensemble partiellement ordonné de Frobenius sur les entiers $\mathbb{Z}$, c.à.d. que pour un sous-semigroupe $\Lambda$ de les entiers non-négatifs $(\mathbb{N},+)$ nous définissons l'ordre par $n \leq_{\Lambda} m$ si $m-n \in \Lambda$. Quand le $\Lambda$ est engendré par deux nombres $a$ et $b$, relativement premiers entre eux, nous montrons que le complexe des chaînes d'un intervalle quelconque dans l'ensemble partiellement ordonné de Frobenius est soit contractible soit homotopiquement équivalent à une sphère. Nous montrons aussi que dans le cas où $\Lambda$ est engendré par les entiers $\{a,a+d,a+2d,\ldots,a+(a-1)d\}$, le complexe des chaînes a le type de homotopie d'un bouquet de sphères.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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