Bibliographic record
Abstract
approximately 20 years ago in connection with the order of certain simple groups. These are the numbers fn which satisfy the recurrence / » i = 6/w-/*-i 0) with initial conditions fi = l and f2 = 7. These numbers have also been studied in other contexts. For example, Bonk, Shapiro, and Simion [2] discuss them in relation to Schroder numbers and combinatorial statistics on lattice paths. Recently, Barcucci et al. [1] provided a combinatorial interpretation for the NSW numbers by defining a certain regular language 2J and studying particular properties of 2J. They close their note by asking two questions: 1. Do there exist infinitely many fn prime? 2. Do there exist infinitely many fn composite? The goal of this paper is to answer the second question affirmatively, but in a much broader context. Fix an integer k>2 and consider the sequence of values satisfying fn+l = kfn~~fn-\\> fi = l9 and f2 = k +1. Then we have the following theorem.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".