Bibliographic record
Abstract
Continued fractions have been a topic of mathematical study for quite some time. For example, Euler devotes a full chapter of his Introductio in Analysin Infinitorum [1] to continued fractions. We give a method of representing the usual construction of finite continued fractions in terms of a grid. This provides a more visual way of viewing continued fractions than one gets with the standard treatments. We hope that this alternative way of representing continued fractions gives new insight into them; in fact, we describe an unsolved problem involving continued fractions in terms of our grid representation. Although the usual treatment of continued fractions is not geometric there are some exceptions. One appears as part of Hancock’s Development of the Minkowski Geometry of Numbers [2] (see Chapters VII and X); however, our representation is different from anything in this work. Another is Klein’s geometric interpretation of the convergents of an infinite continued fraction (see Olds [3, pp. 77–79]); this is also different from what we are trying to do, as we are working only with finite continued fractions.
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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 | 0.001 |
| 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 | 0.001 |
| 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 teacher head, 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".