Bibliographic record
Abstract
The search for an appropriate notion of amenability for inverse semigroups is an ongoing program in operator algebras and related fields.This thesis presents an approach to this problem using the theory of inverse semigroup actions.An inverse semigroup action S X is said to be amenable if the action groupoid S X is amenable as an tale groupoid.We prove two fundamental results from the literature on amenable inverse semigroup actions: firstly, that all actions of an inverse semigroup S are amenable whenever the universal action S S 0 is amenable; and secondly, that the universal action of an inverse semigroup S is amenable whenever S admits an idempotent-pure partial homomorphism into an amenable group.These results are applied to show that all actions of graph inverse semigroups and abelian inverse semigroups are amenable, and to show that the universal action of the free inverse semigroup on two generators is not amenable.We also introduce an intrinsic action of an inverse semigroup on its Stone-ech compactification, give an inverse semigroup model for Willett's HLS groupoids, and produce an example of an inverse semigroup W which witnesses weak containment but fails to have an amenable universal action.i Chapter 2 PreliminariesIn this chapter, we discuss some of the general theory of tale groupoids, inverse semigroups, and inverse semigroup actions.We will begin with an introduction to topological and tale groupoids, and provide a brief survey of the equivalent conditions of amenability for tale groupoids.We state several sufficient conditions for an tale groupoid to be amenable, providing detailed proofs where possible.We then give a thorough introduction to the elementary theory of inverse semigroups, assuming that the reader has no background knowledge on the subject.We conclude the chapter by developing important preliminary results for the Stone-ech compactification of a discrete space, which will be used in Chapter 3. tale GroupoidsThis section develops the general theory of tale groupoids.Our reference for the definitions and results found in this section is [39].Definition 2.1.1.A groupoid is a set G equipped with a distinguished family of pairs G (2) G G (called the set of composable pairs), together with a multiplication operation G (2) (, ) G and an inverse map G -1 G such that
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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 | 0.001 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".