On<i>E</i>-discretization of tori of compact simple Lie groups
Bibliographic record
Abstract
Three types of numerical data are provided for compact simple Lie groups G of classical types and of any rank. These data are indispensable for Fourier-like expansions of multidimensional digital data into finite series of E -functions on the fundamental domain F e . Firstly, we determine the number | F e M | of points in F e from the lattice P ∨ M , which is the refinement of the dual weight lattice P ∨ of G by a positive integer M . Secondly, we find the lowest set Λ e M of the weights, specifying the maximal set of E -functions that are pairwise orthogonal on the point set F e M . Finally, we describe an efficient algorithm for finding the number of conjugate points to every point of F e M . Discrete E -transform, together with its continuous interpolation, is presented in full generality.
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How this classification was reachedexpand
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 | 0.002 |
| 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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".