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
1. It is tempting to believe that any sequence (?n) that is C6saro-convergent in probability necessarily has a subsequence that is a.s. C6saro-convergent. This is not true however. As an example, take an independent identically distributed sequence that satisfies the weak but not the strong law of large numbers (e.g., any symmetric distribution without first moment but with tails slightly smaller than Cauchy). 2. If we drop the nonnegativity, Observation 1 becomes false. Consider, for example, the constants (1)n log n. But if every permutation of a sequence of arbitrarily signed random variables is a.s. C6saro-convergent to a finite limit, does the sequence satisfy condition (A)? We do not know. 3. S. D. Chatterji [4] has already given versions of the subsequence theorem for ?n in LP with p < 1, but with a factor n-'/P instead of n-1. A nice review paper is [5]. 4. More recently, E. P6ter [7] gave sufficient criteria describing general distributional limit laws for which a permutation invariant version of the subsequence principle holds, in the same way that Berkes's result improves Koml6s's theorem.
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 | 0.001 | 0.002 |
| 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 | 0.001 |
| 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