Hamiltonian fragmentation in dimension four with application to spectral estimators
Bibliographic record
Abstract
We prove a new Hamiltonian extension and consequently a fragmentation result in dimension [Formula: see text] for the symplectic manifold [Formula: see text]. Polterovich and Shelukhin have recently constructed a family of functionals on the space of time-dependent Hamiltonian functions on [Formula: see text] for rational [Formula: see text], called Lagrangian spectral estimators. Using our fragmentation result we prove that the restriction of their functionals to the subdomain [Formula: see text] is a uniformly [Formula: see text]-continuous functional where [Formula: see text]. As an application of our results, we show that the complement of a Hofer ball in the group of compactly supported Hamiltonian diffeomorphisms of [Formula: see text] contains a [Formula: see text]-open subset. Finally, we show that the aforementioned group equipped with the Hofer distance admits an isometric embedding of an infinite-dimensional flat space for suitable parameters [Formula: see text] and [Formula: see text].
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 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 | 0.001 | 0.001 |
| 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".