Why this work is in the frame
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Bibliographic record
Abstract
Given positive integers $v$, $k$, $t$ and $λ$ with $v \geq k \geq t$, a packing design PD$_λ(v,k,t)$ is a pair $(V,\mathcal{B})$, where $V$ is a $v$-set and $\mathcal{B}$ is a collection of $k$-subsets of $V$ such that each $t$-subset of $V$ appears in at most $λ$ elements of $\mathcal{B}$. When $λ=1$, a PD$_1(v,k,t)$ is equivalent to a binary code with length $v$, minimum distance $2(k-t+1)$ and constant weight $k$. The maximum size of a PD$_λ(v,k,t)$ is called the {packing number}, denoted PDN$_λ(v,k,t)$. In this paper we consider packing designs with $k$ large relative to $v$. We prove that for a positive integer $n$, PDN$_λ(v,k,t) = n$ whenever $nk-(t-1)\binom{n}{λ+1} \leq λv < (n+1)k-(t-1)\binom{n+1}{λ+1}$. We also prove that if no point appears in more than three blocks, then the blocks of a PD$_2(v,k,2)$ can be ordered so that no ordered pair occurs more than once. This produces a directed packing design and we show that the corresponding directed packing number is equal to $n$ when $nk-\binom{n}{3} \leq 2v < (n+1)k-\binom{n+1}{3}$. Such directed packing designs yield $(k-t)$-insertion/deletion codes.
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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 | 0.000 | 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 | 0.001 |
| 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