The Jordan structure of two-dimensional loop models
Bibliographic record
Abstract
We show how to use the link representation of the transfer matrix D N of loop models on the lattice to calculate partition functions, at criticality, of the Fortuin–Kasteleyn model with various boundary conditions and parameter and, more specifically, partition functions of the corresponding Q -Potts spin models, with Q = β 2 . The braid limit of D N is shown to be a central element F N (β) of the Temperley–Lieb algebra TL N (β), its eigenvalues are determined and, for generic β, a basis of its eigenvectors is constructed using the Wenzl–Jones projector. With any element of this basis is associated a number of defects d , 0 ≤ d ≤ N , and the basis vectors with the same d span a sector. Because components of these eigenvectors are singular when and , the link representations of F N and D N are shown to have Jordan blocks between sectors d and d ′ when d − d ′ < 2 b and ( d > d ′). When a and b do not satisfy the previous constraint, D N is diagonalizable.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".