Amenability and Unique Ergodicity of the Automorphism Groups of all Countable Homogeneous Directed Graphs
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Bibliographic record
Abstract
We establish the amenability, unique ergodicity and nonamenability of various automorphism groups from Cherlin's list of countable homogeneous directed graphs. This marks a complete understanding of the amenability of the automorphism groups from this list, and except for the Semigeneric graph case, marks a complete understanding of the unique ergodicity of these groups.\nAlong the way we establish that a certain product of Fraïssé classes preserves amenability, unique ergodicity and the Hrushovski property. We also establish the unique ergodicity of various other automorphism groups of Fraïssé structures that do not appear on Cherlin's list.
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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 | 0.000 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it