Bibliographic record
Abstract
The Levine-Tristram signature is a well-known invariant of links that is topological in nature -- its known definitions rely on manifolds associated with the link and it is related to other topological invariants such as genus, unlinking number, and the Alexander polynomial. In 2018 Kashaev introduced a link invariant defined using a simple algorithm on link diagrams which he conjectured also computes the Levine-Tristram signature [Kas21]. In this thesis we present a method of obtaining Kashaev's invariant using the original Seifert surface definition of the Levine-Tristram signature, making evident the relationship between the two and thereby proving Kashaev's conjecture. We obtain as a corollary another formula for the Alexander polynomial. The content of this thesis is based on [Liu25].
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.020 | 0.004 |
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".