Bibliographic record
Abstract
In the theory of Banach spaces over valued fields developed, for example, in the classical book of van Rooij, Non-archimedean Functional Analysis , the group G G of a valuation on a field K K is a subgroup of the multiplicative subgroup ( R + , ⋅ \mathbb {R}^+, \cdot ). Also, if E E is a K K -vector space, the set of norms of E E is a subset of [ 0 , ∞ ) [0, \infty ) . Yet this theory can be subsumed in a larger one, by allowing G G to be any linearly ordered multiplicative group, and considering the norms of the space as elements of a new structure, a G G -module. Such a setting includes infinite dimensional spaces, where a bilinear form defines a (non-archimedean) norm, the space is complete in the induced topology and the Projection Theorem holds. Time and time again it has turned out that the structure of G G -modules has a strong say in the features of non-archimedean spaces over fields with valuations of arbitrary rank. This paper, that continues a line which started with the work of W. Schikhof and E. Olivos, is the starting point in the study of a particular class of G G -modules, those in which an independent generating set is a convex interval in the order of the G G -module. The authors could not forget to thank Wim Schikhof. It was during his stays in Temuco that this line of research started.
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 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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.004 |
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".