Screw motion surfaces in $\Bbb H\sp 2\times\Bbb R$ and $\Bbb S\sp 2\times\Bbb R$
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
In this paper we study the geometry of constant mean curvature H-screw motion surfaces in H 2 R and S 2 R. We compute the Abresch-Rosenberg holomorphic quadratic differential Q. For instance, if the ambient space is H 2 R, we derive that, given , if 0 < 4H 2 < 1, then there exists a complete H-screw motion surface with pitch immersed in H 2 R, such that Q = 0. An analogous result holds if the ambient space is S 2 R. We deduce a general non-parametric formula for the mean curvature H(). When H is constant, we find a first integral and use it to get an explicit two parameter family of complete, embedded, simply connected, minimal screw motion surfaces in H 2 R with pitch . If = 1, each such surface has Gaussian curvature K -1. We deduce that any two isometric screw motion minimal immersions in H 2 R or S 2 R are associate, i.e., the absolute values of their Hopf functions are the same.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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