Influence of Divisor-ratio to Distribution of Semiprime's Divisor
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Bibliographic record
Abstract
For a semiprime that consists in two distinct odd prime divisors, this article makes an investigation on the distribution of the small divisor by analyzing the divisor-ratio that is calculated by the big divisor divided by the small one. It proves that, the small divisor must be a divisor of an odd integer lying in an interval that is uniquely determined by the divisor-ratio, and the length of the interval decreases exponentially with the increment of the ratio. Accordingly, a big divisor-ratio means the small divisor can be found in a small interval whereas a small divisor-ratio means it has to find the small divisor in a large interval. The proved theorems and corollaries can provide certain theoretical supports for finding out the small divisor of the semiprime.
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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 | 0.005 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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