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
The existence of a family of nilmanifolds which possess riemannian metrics with Liouville-integrable geodesic flow is demonstrated. These homogeneous spaces are of the form D\H, where if is a connected, simply-connected two-step nilpotent Lie group and D is a discrete, cocompact subgroup of H. The metric on D\H is obtained from a left-invariant metric on H. The topology of these nilmanifolds is quite rich; in particular, the first example of a Liouville-integrable geodesic flow on a manifold whose fundamental group possesses no commutative subgroup of finite index is obtained. It is shown that several of the conclusions of Taimanov's theorems on the topology of manifolds with real-analytically Liouville-integrable geodesic flows do not obtain in the smooth category DEFINITION 1.1 (Liouville Integrability). The hamiltonian vector field XH is Liouville integrable on (L 2k ,uj) if there exists a smooth function F := (/i = H,... , fk) :
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.018 | 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 it