-algebras of labelled graphs III—-theory computations
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Bibliographic record
Abstract
In this paper we give a formula for the $K$ -theory of the $C^{\ast }$ -algebra of a weakly left-resolving labelled space. This is done by realizing the $C^{\ast }$ -algebra of a weakly left-resolving labelled space as the Cuntz–Pimsner algebra of a $C^{\ast }$ -correspondence. As a corollary, we obtain a gauge-invariant uniqueness theorem for the $C^{\ast }$ -algebra of any weakly left-resolving labelled space. In order to achieve this, we must modify the definition of the $C^{\ast }$ -algebra of a weakly left-resolving labelled space. We also establish strong connections between the various classes of $C^{\ast }$ -algebras that are associated with shift spaces and labelled graph algebras. Hence, by computing the $K$ -theory of a labelled graph algebra, we are providing a common framework for computing the $K$ -theory of graph algebras, ultragraph algebras, Exel–Laca algebras, Matsumoto algebras and the $C^{\ast }$ -algebras of Carlsen. We provide an inductive limit approach for computing the $K$ -groups of an important class of labelled graph algebras, and give examples.
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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 | 0.003 | 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 | 0.000 |
| 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 it