On Minimal Length Factorizations of Finite Groups
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Bibliographic record
Abstract
Logarithmic signatures are a special type of group factorizations,\nintroduced as basic components of certain cryptographic keys.\nThus, short logarithmic signatures are of special interest.\nWe deal with the question of finding logarithmic signatures of\nminimal length in finite groups. In particular, such factorizations\nexist for solvable, symmetric, and alternating groups.\n¶ We show how to use the known examples to derive minimal\nlength logarithmic signatures for other groups. Namely, we prove\nthe existence of such factorizations for several classical groups\nand---in parts by direct computation---for all groups of order\n<175,560 ($=\\ord(J_1)$, where $J_1$ is Janko's first sporadic simple group). Whether there exists a minimal length logarithmic signature for each finite group still remains an open question.
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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 | 0.002 |
| 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) | 0.001 | 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