Iterated integrals, diagonal cycles and rational points on elliptic curves
Bibliographic record
Abstract
The theme of this article is the connection between the pro-unipotent fundamental group 1(X; o) of a pointed algebraic curve X, algebraic cycles, iterated integrals, and special values of L-functions. The extension of mixed Hodge structures arising in the second stage in the lower central series of 1(X; o) gives rise to a supply of complex points on the Jacobian Jac(X) of X indexed by Hodge cycles on X X. The main results of this note relate these points to the Abel-Jacobi image of Gross-Kudla-Schoen's modified diagonal in X 3 , and express this Abel-Jacobi image in terms of iterated integrals. The resulting formula is the basis for the practical complex-analytic calculations of these points when X is a modular (or Shimura) curve, a setting where the recent work [YZZ] of X. Yuan, S. Zhang and W. Zhang relates their non-triviality to special values of certain L-series attached to modular forms.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".