Recursive and Cyclic Constructions for Double‐Change Covering Designs
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Bibliographic record
Abstract
ABSTRACT A double‐change covering design (DCCD) is a ‐set and an ordered list of blocks of size where every pair from must occur in at least one block and each pair of consecutive blocks differs by exactly two elements. It is minimal if it has the fewest blocks possible and circular when the first and last blocks also differ by two elements. We give a recursive construction that uses 1‐factorizations of complete graphs and expansion sets to construct a DCCD() from a DCCD(). We construct circular DCCD() and circular DCCD() from single‐change covering designs and determine minimum DCCD when . We use difference like methods to construct five infinite families of minimum circular DCCD() when for any . The recursive construction is then used to build twelve additional minimum DCCD from members of these infinite families. Finally, the difference like method is used to construct a minimum circular DCCD(61,4,366).
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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 | 0.000 |
| 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