Orbit equivalence rigidity for product actions
Why this work is in the frame
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Bibliographic record
Abstract
In this talk we provide a natural complement to Monod and Shalom's orbit equivalence superrigidity theorem for irreducible actions of product groups by providing a large class of product actions whose orbit equivalence relation remember the product structure. More precisely, we show that if a product $\\Gamma_1\\times\\dots\\times\\Gamma_n \\curvearrowright X_1\\times\\dots\\times X_n$ of measure preserving actions is stably orbit equivalent to a measure preserving action $\\Lambda\\curvearrowright Y$, then $\\Lambda\\curvearrowright Y$ is induced from an action $\\Lambda_0\\curvearrowright Y_0$ and there exists a direct product decomposition $\\Lambda_0=\\Lambda_1\\times\\dots\\times\\Lambda_n$ into $n$ infinite groups. Moreover, there exists a measure preserving action $\\Lambda_i\\curvearrowright Y_i$ that is stably orbit equivalent to $\\Gamma_i\\curvearrowright X_i$, for any $1\\leq i\\leq n$, and the product action $\\Lambda_1\\times\\dots\\times\\Lambda_n\\curvearrowright Y_1\\times\\dots\\times Y_n$ is isomorphic to $\\Lambda_0\\curvearrowright Y_0$.
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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 | 0.001 |
| 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