The structure of invariant α-CP multilinear maps and associated<i>J</i>-representations
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we introduce a notion of -completely positive multilinear maps as a generalization of completely positive multilinear maps. We construct a Krein space representation associated with an invariant -completely positive multilinear map and show that the natural ordering of invariant -completely positive multilinear maps is characterized in terms of the Radon–Nikodým derivatives. Finally, we construct a covariant Krein space representation associated with covariant and invariant -completely positive multilinear maps and show that a covariant and invariant -completely positive multilinear map on -algebras can be extended to an -completely positive multilinear map on -crossed products.
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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 | 0.001 | 0.004 |
| 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