Bibliographic record
Abstract
A Costas array is a permutation array for which the vectors joining pairs of 1s are all distinct. We propose a new 3-D combinatorial object related to Costas arrays: an order $n$ Costas cube is an array $(d_{i,j,k})$ of size $n \times n \times n$ over $\mathbb {Z}_{2}$ for which each of the three projections of the array onto two dimensions, namely $\left({\sum _{i} d_{i,j,k}}\right)$ and $\left({\sum _{j} d_{i,j,k}}\right)$ and $\left({\sum _{k} d_{i,j,k}}\right)$ , is an order $n$ Costas array. We determine all Costas cubes of order at most 29, showing that Costas cubes exist for all these orders except 18 and 19 and that a significant proportion of the Costas arrays of certain orders occur as projections of Costas cubes. We then present constructions for four infinite families of Costas cubes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.003 |
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".