Bibliographic record
Abstract
Whereas Alan Day showed that the continuous lattices are the algebras of a filter monad on Set , we employ the theory of lax algebras (as developed by Barr, Pisani, Clementino, Hofmann, Tholen, Seal and others) to broaden this characterisation to a description of the wider class of continuous dcpos as algebras of a lax filter monad. Building on an axiomatisation of topological spaces through convergence as lax algebras of a lax extension of the filter monad to a category of relations, we show that those topological spaces whose associated lax algebra is in fact a strict algebra are what M. Erné called the C-spaces . The sober C-spaces are precisely the continuous dcpos under the Scott topology, and we discuss how the possibly little-known C-spaces, which have been studied by B. Banaschewski, J. D. Lawson, R.-E. Hoffmann, M. Erné and G. Wilke, very directly capture an essential topological notion of approximation inherent in the continuous dcpos, and hence provide a natural topological concept of domain.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.000 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| 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".