The Endoscopic Classification of Representations
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
We shall outline a classification [A] of the automorphic representations of special orthogonal and symplectic groups in terms of those of general linear groups. This necessarily includes a classification of local L-packets of representations. It also requires a classification of the extended packets that are the local constituents of nontempered automorphic representations. Our description will be brief. In particular, we will restrict it to quasisplit ∗ orthogonal and symplectic groups G, even though at least some of the results can be extended (not without effort) to inner twists of G. The methods rest ultimately on two comparisons of trace formulas. One is the spectral identity that is the end product of the stabilization of the trace formula for G. This was established some years ago [A1], under the assumption of the fundamental lemma. It now holds without condition, thanks to the work of Waldspurger [W1][W2], the recent breakthrough by Ngo [N], and the extensions of Chaudouard and Laumon [CL1] [CL2]. The other is the spectral identity given by the stabilization of the twisted trace formula for GL(N). This formula is still conditional. The relevant twisted fundamental lemmas are now known [W3], [W4], at least up to the twisted variants of [CL1] and [CL2]. The problem is to develop twisted generalizations of the techniques of [A1] and related papers. Until this is done, the results we describe here have also to be regarded as conditional. We take F to be a local or global field of characteristic 0, and G to be a quasisplit, special orthogonal or symplectic group over F. Then G has a complex dual group G, and a corresponding
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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.006 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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