Bibliographic record
Abstract
Abstract We study the cohomology of connected components of Shimura varieties coming from the group GSp 2g , by an approach modeled on the stabilization of the twisted trace formula, due to Kottwitz and Shelstad. More precisely, for each character ϖ on the group of connected components of we define an operator L ( ω ) on the cohomology groups with compact supports H i c ( , ), and then we prove that the virtual trace of the composition of L ( ω ) with a Hecke operator f away from p and a sufficiently high power of a geometric Frobenius , can be expressed as a sum of ω - weighted (twisted) orbital integrals (where ω - weighted means that the orbital integrals and twisted orbital integrals occuring here each have a weighting factor coming from the character ϖ ). As the crucial step, we define and study a new invariant α 1 ( γ 0 ; γ, δ ) which is a refinement of the invariant α ( γ 0 ; γ, δ ) defined by Kottwitz. This is done by using a theorem of Reimann and Zink.
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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 | 0.000 | 0.002 |
| 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) | 0.001 | 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".