Bibliographic record
Abstract
All the fibres of a fibre bundle are, by definition, diffeomorphic to each other. In the absence of additional structure, however, there is no canonical way to single out a particular diffeomorphism between fibres. In the case of a product bundle, for example, such a special choice is indeed available because of the existence of the second projection map onto the typical fibre. In this extreme case, we may say that we are in the presence of a canonical distant parallelism in the fibre bundle. An equivalent way to describe this situation is by saying that we have a canonical family of non-intersecting smooth cross sections such that each point in the fibre bundle belongs to one, and only one, of them. In a general fibre bundle we can only afford this luxury noncanonically and locally. A connection on a fibre bundle is, roughly speaking, an additional structure defined on the bundle that permits to establish intrinsic fibre diffeomorphisms for fibres lying along curves in the base manifold. In other words, a connection can be described as a curve-dependent parallelism. Given a connection, it may so happen that the induced fibre parallelisms turn out to be curve-independent. A quantitative measure of this property or the lack thereof is provided by the vanishing, or otherwise, of the curvature of the connection.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.023 | 0.008 |
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".