Bibliographic record
Abstract
Given an algebraic action of a semigroup, we construct an inverse semigroup, and we characterize Hausdorffness, topological freeness, and minimality of the associated tight groupoid in terms of conditions on the initial algebraic action. We parameterize all closed invariant subspaces of the unit space of our groupoid, and characterize topological freeness of the associated reduction groupoids. We prove that our groupoids are purely infinite whenever they are minimal, which answers a general open question in the affirmative for our special class of groupoids. In the topologically free case, we prove that the concrete C*-algebra associated with the algebraic action is always a (possibly exotic) groupoid C*-algebra in the sense that it sits between the full and essential C*-algebras of our groupoid. This provides a framework for studying such concrete C*-algebras, allowing us to obtain structural results that were only previously available for very special classes of algebraic actions. For instance, we obtain results on simplicity and pure infiniteness for C*-algebras associated with subshifts over semigroups, actions coming from commutative algebra, and non-commutative rings. These results were out of reach using existing techniques.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| 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) | 0.001 | 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".