Fast combined multiple recursive generators with multipliers of the form a = ±2q ±2r
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Bibliographic record
Abstract
We study a class of combined multiple recursive random number generators constructed in a way that each component runs fast and is easy to implement, while the combination enjoys excellent structural properties as measured by the spectral test. Each component is a linear recurrence of order k > 1, modulo a large prime number, and the coefficients are either 0 or are of the form a = ±2q or a = ±2q ±2r. This allows a simple and very fast implementation, because each modular multiplication by a power of 2 can be implemented via a shift, plus a few additional operations for the modular reduction. We select the parameters in terms of the performance of the combined generator in the spectral test. We provide a specific implementation.
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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 | 0.001 |
| Open science | 0.001 | 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