Bibliographic record
Abstract
We study certain arithmetic group cocycles valued in differential forms arising from torus bundles over (locally) symmetric spaces, which we call Eisenstein theta lifts following the nomenclature of Bergeron-Charollois-Garcia, who constructed them using automorphic theta kernels arising from regularized Eisenstein series.By studying the Hodge theory of such torus bundles in the setting where they have the structure of an abelian family, we establish that these analytically constructed cocycles agree with the cohomology classes defined by Kings-Sprang using equivariant polylogarithm classes in coherent cohomology, showing the former have a natural integral structure and giving an analytic way to compute the latter.We then construct analogous cohomology classes (called by analogy arithmetic theta lifts) valued in Milnor K-theory using a motivic analogue of the equivariant polylogarithm, and show their de Rham regulators yield the Eisenstein theta lift.R SUM . Nous tudions des cocycles pour des groupes arithmtiques valeurs dans des formes diffrentielles sur des tores fibres au-dessus des espaces (localement) symmtriques, que nous appelons des relvements thta d'Eisenstein aprs Bergeron-Charollois-Garcia, qui les ont construits en utilisant des noyaux thta automorphiques venant des sries d'Eisenstein rgularises.En tudiant la thorie de Hodge dans le cas des fibrs abliens, nous dmontrons que les classes de ces cocycles analytiques sont donnes par les classes abstraites dfinies par Kings-Sprang en utilisant le polylogarithme quivariant en cohomologie cohrente.Cela implique que les cocycles analytiques ont une structure intgrale canonique, et en mme temps donne un fac on de calculer les classes abstraites.Ensuite, nous construisons des classes abstraites analogues (appeles relvements d'Eisenstein arithmtiques) valeurs dans la K-thorie de Milnor en utilisant le polylogarithme quivariant dans le contexte motivique, puis dmontrons que leurs rgulateurs sont donns par les relvements d'Eisenstein.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.000 | 0.003 |
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".