The weak circular repetition threshold over large alphabets
Why this work is in the frame
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Bibliographic record
Abstract
The repetition threshold for words on n letters, denoted RT( n ), is the infimum of the set of all r such that there are arbitrarily long r -free words over n letters. A repetition threshold for circular words on n letters can be defined in three natural ways, which gives rise to the weak , intermediate , and strong circular repetition thresholds for n letters, denoted CRT W ( n ), CRT I ( n ), and CRT S ( n ), respectively. Currie and the present authors conjectured that CRT I ( n ) = CRT W ( n ) = RT( n ) for all n ≥ 4. We prove that CRT W ( n ) = RT( n ) for all n ≥ 45, which confirms a weak version of this conjecture for all but finitely many values of n .
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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