Bibliographic record
Abstract
In this thesis we provide a description of the first paper on Beyond Endoscopy by Altug and explain how to generalize to totally real fields, based on a joint work of the author with Melissa Emory, Debanjana Kundu and Tian An Wong, and is a work in preparation. This part is mostly expository, and we refer the reader to the relevant paper. Furthermore, we prove a conjecture of Arthur. In his original paper on Beyond Endoscopy, Langlands provides a formula for certain product of orbital integrals in GL(2, Q), subsequently used by Altug to manipulate the regular elliptic part of the trace formula with the goal of isolating the contribution of the trivial representation. Arthur predicts this formula should coincide with a product of polynomials associated to zeta functions of orders constructed by Zhiwei Yun. We prove this is the case by finding the explicit polynomials and recovering the original formula from them. We also explain how some aspects of the strategy used can be interpreted as problems of independent interest and importance of their own. En esta tesis damos una descripción del primer articulo sobre Más Alla de la Endoscopía por Altug y explicamos como generalizarlo a campos totalmente reales, basados en un trabajo conjunto con Melissa Emory, Debanjana Kundu y Tian An Wong, y él cuál sigue en estado de preparación. Esta parte es mayormente una exposición y referimos al lector al artículo relevante. Además, demostramos una conjetura de Arthur. En su artículo original sobre Más Allá de la Endoscopía, Langlands da una fórmula para cierto productos de integrales de órbita en GL(2, Q), subsecuentemente utilizadas por Altug para manipular la parte regular eliptica de la formula de traza con el objectivo de aislar la contribución de la representación trivial. Arthur predice que esta formula coincide con un producto de polinomios asociados a funciones zeta de órdenes construidos por Zhiwei Yun. Demostramos que esto es cierto mediante hallar los polinomios explicitos y recuperamos la formula original a partir de ellos. Más aún, también explicamos como algunos aspectos de esta estrategia pueden ser interpretados como problemas de interés e importancia independiente.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.029 | 0.002 |
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; both teacher heads agree on what is shown here.
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".