Classifying sufficiently connected PSC manifoldsin 4 and 5 dimensions
Bibliographic record
Abstract
We show that if N is a closed manifold of dimension n D 4 (resp.n D 5) with 2 .N / D 0 (resp. 2 .N / D 3 .N / D 0) that admits a metric of positive scalar curvature, then a finite cover y N of N is homotopy equivalent to S n or connected sums of S n 1 S 1 .Our approach combines recent advances in the study of positive scalar curvature with a novel argument of Alpert, Balitskiy and Guth.Additionally, we prove a more general mapping version of this result.In particular, this implies that if N is a closed manifold of dimensions 4 or 5, and N admits a map of nonzero degree to a closed aspherical manifold, then N does not admit any Riemannian metric with positive scalar curvature.53C21
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".