Bibliographic record
Abstract
During the period from the end of the 1960s through to the beginning of the 1970s, Conway pursued the objective of forming a complete table of knots. As we have seen in our discussions thus far, the knot invariants that had been discovered up to that point in time were not sufficient to accomplish this aim. Therefore, Conway pulled another jewel from his bag of cornucopia and introduced the concept of a tangle. Using this variation on a knot, a new class of knots could be defined: algebraic knots. By studying this class of knots, various Local problems were able to be solved, which led to a further jump in the level of understanding of knot theory. However, since there are knots that are not algebraic, the complete classification of knots could not be realized. Nevertheless, the introduction of this new research approach has had a significant impact on knot theory. In this chapter we shall investigate 2-bridge knots (or links), which are a special kind of algebraic knot obtained from trivial tangles.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 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".