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 prove a new version of isoperimetric inequality: Given a positive real m, a Banach space B, a closed subset Y of metric space X, and a continuous map f:Y→B with f(Y) compact infFHCm+1(F(X))≤c(m)HCm(f(Y))m+1 m, where HCm denotes the m-dimensional Hausdorff content, the infimum is taken over the set of all continuous maps F:X⟶B such that F(y)=f(y) for all y∈Y, and c(m) depends only on m. Moreover, one can find F with a nearly minimal HCm+1 such that its image lies in the C(m)HCm(f(Y))1 m-neighborhood of f(Y) with the exception of a subset with zero (m+1)-dimensional Hausdorff measure. The paper also contains a very general coarea inequality for Hausdorff content and its modifications. As an application we demonstrate an inequality conjectured by Larry Guth that relates the m-dimensional Hausdorff content of a compact metric space with its (m−1)-dimensional Urysohn width. We show that this result implies new systolic inequalities that both strengthen the classical Gromov’s systolic inequality for essential Riemannian manifolds and extend this inequality to a wider class of non-simply-connected manifolds.
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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.004 |
| Insufficient payload (model declined to judge) | 0.027 | 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