Bibliographic record
Abstract
The two faces of the twisted Kummer surface by Adam Logan (Montral, QC) 1. Introduction. Let C be a curve of genus 2 defined by an equation of the form y 2 = f (x) over a number field F . In studying the arithmetic of C, it is necessary to consider the Jacobian Jac(C) of C, an abelian variety of dimension 2. However, this variety is rather difficult to compute with directly (it is most naturally embedded into projective space as the intersection of 72 quadrics in P 15 ). Accordingly, one often considers the quotient of Jac(C) by the involution -1 that takes the class of a divisor D to the class of -D. This quotient, the Kummer surface of C, can be embedded as a quartic surface in P 3 with 16 nodes; this is the largest number of isolated singularities possible for a quartic surface in P 3 . The minimal desingularization of the quotient can also be embedded as the intersection of three quadrics in P 5 .
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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 | 0.000 |
| 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 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".