Semiflows “Monotone with Respect to High-Rank Cones" on a Banach Space
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
We consider semiflows in general Banach spaces motivated by monotone cyclic feedback systems or differential equations with integer-valued Lyapunov functionals. These semiflows enjoy strong monotonicity properties with respect to “cones” of high ranks, which imply order-related structures on the $\omega$-limit sets of precompact semiorbits. We show that for a pseudoordered precompact semiorbit the $\omega$-limit set $\omega(x)$ either is ordered, or is contained in the set of equilibria, or possesses a certain ordered homoclinic property. In particular, we show that if $\omega(x)$ contains no equilibrium, then $\omega(x)$ is ordered, and hence the dynamics of the semiflow on $\omega(x)$ is topologically conjugate to a compact flow on $\mathbb{R}^k$ with $k$ being the rank. We also establish a Poincaré--Bendixson-type theorem in the case where $k=2$. All our results are established without the smoothness condition on the semiflow, allowing applications to many cellular or physiological feedback systems with piecewise linear vector fields and to infinite-dimensional systems where the $C^1$-closing lemma or smooth manifold theory has not been developed.
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 | 0.001 |
| 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) | 0.001 | 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