Why this work is in the frame
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Bibliographic record
Abstract
We establish connections between the lattices of non-crossing partitions of type B introduced by V. Reiner, and the framework of the free probability theory of D. Voiculescu. Lattices of non-crossing partitions (of type A, up to now) have played an important role in the combinatorics of free probability, primarily via the non-crossing cumulants of R. Speicher. Here we introduce the concept of <italic>non-crossing cumulant of type B;</italic> the inspiration for its definition is found by looking at an operation of “restricted convolution of multiplicative functions”, studied in parallel for functions on symmetric groups (in type A) and on hyperoctahedral groups (in type B). The non-crossing cumulants of type B live in an appropriate framework of “non-commutative probability space of type B”, and are closely related to a type B analogue for the R-transform of Voiculescu (which is the free probabilistic counterpart of the Fourier transform). By starting from a condition of “vanishing of mixed cumulants of type B”, we obtain an analogue of type B for the concept of free independence for random variables in a non-commutative probability space.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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