Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract. For a finite real reflection group W and a W-orbit O of flats in its reflection arrangement – or equivalently a conjugacy class of its parabolic subgroups – we introduce a statistic noninvO(w) on w in W that counts the number of “O-noninversions ” of w. This generalizes the classical (non-)inversion statistic for permutations w in the symmetric group Sn. We then study the operator νO of right-multiplication within the group algebra CW by the element that has noninvO(w) as its coefficient on w. We reinterpret νO geometrically in terms of the arrangement of reflecting hyperplanes for W, and more generally, for any real arrangement of linear hyperplanes. At this level of generality, one finds that, after appropriate scaling, νO corresponds to a Markov chain on the chambers of the arrangement. We show that νO is self-adjoint and positive semidefinite, via two explicit factorizations into a symmetrized form pitpi. In one such factorization, the matrix pi is a generalization of the projection of a simplex onto the linear ordering polytope from the theory of social choice. In the other factorization of νO as pitpi, the matrix pi is the transition matrix for one of the well-studied Bidigare-Hanlon-Rockmore random walks on the chambers of an ar-
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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