Bibliographic record
Abstract
Abstract A p -arithmetic subgroup of $\mathbf {SL}_2(\mathbb {Q})$ like the Ihara group $\Gamma := \mathbf {SL}_2(\mathbb {Z}[1/p])$ acts by Möbius transformations on the Poincaré upper half plane $\mathcal H$ and on Drinfeld’s p -adic upper half plane ${\mathcal H_p := \mathbb {P}_1(\mathbb {C}_p)-\mathbb {P}_1(\mathbb {Q}_p)}$ . The diagonal action of $\Gamma $ on the product is discrete, and the quotient $\Gamma \backslash (\mathcal H_p\times \mathcal H)$ can be envisaged as a ‘mock Hilbert modular surface’. According to a striking prediction of Neková $\check {\text {r}}$ and Scholl, the CM points on genuine Hilbert modular surfaces should give rise to ‘plectic Heegner points’ that encode nontrivial regulators attached, notably, to elliptic curves of rank two over real quadratic fields. This article develops the analogy between Hilbert modular surfaces and their mock counterparts, with the aim of transposing the plectic philosophy to the mock Hilbert setting, where the analogous plectic invariants are expected to lie in the alternating square of the Mordell–Weil group of certain elliptic curves of rank two over $\mathbb {Q}$ .
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 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; a candidate call from one source (direct Gemma or distilled Codex), 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".