Minimizing the mean projections of finite $\rho$-separable packings
Bibliographic record
Abstract
A packing of translates of a convex body in the $d$-dimensional Euclidean space $\mathbb{E}^d$ is said to be totally separable if any two packing elements can be separated by a hyperplane of $\mathbb{E}^{d}$ disjoint from the interior of every packing element. We call the packing $\mathcal P$ of translates of a centrally symmetric convex body $\mathbf{C}$ in $\mathbb{E}^d$ a $\rho$-separable packing for given $\rho\geq 1$ if in every ball concentric to a packing element of $\mathcal P$ having radius $\rho$ (measured in the norm generated by $\mathbf{C}$) the corresponding sub-packing of $\mathcal P$ is totally separable. The main result of this paper is the following theorem. Consider the convex hull $\mathbf{Q}$ of $n$ non-overlapping translates of an arbitrary centrally symmetric convex body $\mathbf{C}$ forming a $\rho$-separable packing in $\mathbb{E}^d$ with $n$ being sufficiently large for given $\rho\geq 1$. If $\mathbf{Q}$ has minimal mean $i$-dimensional projection for given $i$ with $1\leq i
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".