Bibliographic record
Abstract
This paper is based on the article “The self-counting identity”, published in the Fibonacci Quarterly in May 2017, vol. 55 and can be considered as its continuation.In the beginning, we define the “self-counting flow Φ”, which represents a tool for getting from one positive integer sequence to a corresponding other one. It is -so to saya flow on all positive integer sequences and thereby the self-counting sequence {ak } ∞ k=1 = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4, …} shows itself as a unique fixed point.Various methods allow us to study the properties of the flow Φ such as its trajectories and the attraction of its fixed point. We also examine whether the self-counting sequence {a k } ∞ k=1 is the point of convergence of each positive integer sequence under a repeated application of the self-counting flow Φ.At the end of this article, we show some properties of other flows on positive integer sequences, for example those of the “Fibonacci flow F”.
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.
How this classification was reachedexpand
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 | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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; both teacher heads agree on what is shown here.
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".