Why this work is in the frame
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Bibliographic record
Abstract
ABSTRACT. Let β ∈ (1, 2) be a Pisot number and let Hβ denote Garsia’s entropy for the Bernoulli convolution associated with β. It is well known that Hβ < 1 for any Pisot β (see [5]); for the Pisot numbers which satisfy x m = x m−1 + x m−2 + · · · + x + 1 (with m ≥ 2) Garsia’s entropy has been evaluated with high precision, and it proves to be close to 1 – see [1, 6]. No other numerical values for Hβ are known. In the present paper we show that Hβ> 0.81 for all Pisot β and improve this lower bound for certain ranges of β. Our method is based on finding a good upper bound for the maximal growth exponent for the expansions in base β.
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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 | 0.001 |
| 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) | 0.000 | 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