Why this work is in the frame
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Bibliographic record
Abstract
.We study the third moment for functions on arbitrary compact Lie groups. We use techniques of representation theory to generalize the notion of band-limited functions in classical Fourier theory to functions on the compact groups \(\operatorname{SU}(n), \operatorname{SO}(n),\operatorname{Sp}(n)\) . We then prove that for generic band-limited functions the third moment or its Fourier equivalent, the bispectrum, determines the function up to translation by a single unitary matrix. Moreover, if \(G=\operatorname{SU}(n)\) or \(G=\operatorname{SO}(2n+1)\) , we prove that the third moment determines the \(G\) -orbit of a band-limited function. As a corollary, we obtain a large class of finite-dimensional representations of these groups for which the third moment determines the orbit of a generic vector. When \(G=\operatorname{SO}(3)\) this gives a result relevant to cryo-EM, which was our original motivation for studying this problem.Keywordsorbit recoverybispectrumMSC codes94A1222D10
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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 | 0.000 |
| 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