Bibliographic record
Abstract
Let K be a compact set in the complex plane, such that its complement in the Riemann sphere, (ℂ ∪ {∞}) / K , is connected. Also, let U ⊂ ℂ be an open set which contains K . Then there exists a simply connected open set V ⊂ ℂ such that K ⊂ V ⊂ U . We show that if K is replaced by a closed set F ⊂ ℂ, then the preceding result is equivalent to the fact that F is an Arakelian set in ℂ. This holds in more general case when ℂ is replaced by any simply connected open set Ω ⊂ ℂ. In the case of an arbitrary open set Ω ⊂ ℂ, the above extends to the one point compactification of Ω . If we do not require (ℂ ∪ {∞}) / K to be connected, we can demand that each component of (ℂ ∪ {∞}) / V intersects a prescribed set A containing one point in each component of (ℂ ∪ {∞}) / K . Using the previous result, we prove that again if we replace K by a closed set F , the latter is equivalent to the fact that F is a set of uniform meromorphic approximation with poles lying entirely in A .
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".