Adequate links in thickened surfaces and the generalized Tait conjectures
Bibliographic record
Abstract
We apply Kauffman bracket skein algebras to develop a theory of skein adequate links in thickened surfaces.We show that any alternating link diagram on a surface is skein adequate.We apply our theory to establish the first and second Tait conjectures for adequate links in thickened surfaces.Our notion of skein adequacy is broader and more powerful than the corresponding notions of adequacy previously considered for link diagrams in surfaces.For a link diagram D on a surface † of minimal genus g. †/, we show that span.ŒD † / Ä 4c.D/ C 4jDj 4g.†/;where ŒD † is its skein bracket, jDj is the number of connected components of D, and c.D/ is the number of crossings.This extends a classical result of Kauffman, Murasugi and Thistlethwaite.We further show that the above inequality is an equality if and only if D is weakly alternating.This is a generalization of a well-known result for classical links due to Thistlethwaite.Thus, the skein bracket detects the crossing number for weakly alternating links.As an application, we show that the crossing number is additive under connected sum for adequate links in thickened surfaces.
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 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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".