Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This paper develops a new description of the asymptotics for the empirical distributions of significands and significant digits associated with [Formula: see text], where [Formula: see text] denotes the [Formula: see text]th prime number. The work utilizes the space of probability measures on the significand, endowed with a suitable Kantorovich metric, as well as finite-dimensional projections thereof. For sequences sufficiently close to [Formula: see text], it is shown that the limit points of the associated empirical distributions form a circle that is made up of all rescalings of a single absolutely continuous distribution, and is centered at a distribution known as Benford’s law (BL). The precise rate of convergence to that circle is determined. Moreover, even in the infinite-dimensional setting of significands the convergence is seen to occur along a distinguished low-dimensional object, in fact, along a smooth curve intimately related to BL. By connecting [Formula: see text] and BL in a new way, the results rigorously confirm well-documented experimental observations and complement known facts in the literature.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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