A class of cyclic (v; k<sub>1</sub>, k<sub>2</sub>, k<sub>3</sub>; λ) differencefamilies with v ≡ 3 (mod 4) a prime
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Bibliographic record
Abstract
Abstract We construct several new cyclic (v; k1, k2, k3; λ) difference families, with v ≡ 3 (mod 4) a prime and λ = k1 + k2 + k3 − (3v − 1)/4. Such families can be used in conjunction with the well-known Paley-Todd difference sets to construct skew-Hadamard matrices of order 4v. Our main result is that we have constructed for the first time the examples of skew Hadamard matrices of orders 4 · 239 = 956 and 4 · 331 = 1324.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it