A Conjecture about the Analytical Behaviour of Eisenstein Series
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
This paper will formulate and offer evidence for a conjecture on the analytical behaviour of residual Eisenstein series in the positive Weyl chamber. It should play a major role in an also conjectural Paley-Wiener theorem about the Schwartz space of arithmetic quotients. If things work out as I expect, this development should be logically independent of Chapter 7 of [Langlands:1976], and in the end one should obtain a new proof of Langlands ’ completeness theorem. Suppose G to be the group of real points on a reductive group defined over Q and further set Γ an arithmetic subgroup of G K a maximal compact subgroup of G ZG the centre of G For a rational parabolic subgroup P, set N = NP its unipotent radical M =MP its reductive quotient P/NP ΓM the image of Γ ∩ P in M AP the maximal Q-split torus in M δP its modulus character detAdn
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 | 0.000 | 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