Bibliographic record
Abstract
One of our results is a transfer principle between ultrapowers and reduced powers associated with the Fréchet ideal. Although motivated by the Elliott classification programme, this result applies to any axiomatizable category. We also show that there exists a nonprincipal ultrafilter \mathcal{U} on \mathbb{N} such that for every countable (or separable metric) structure B in a countable language the quotient map from the reduced power associated with the Fréchet ideal onto an ultrapower has a right inverse. While the transfer principle is proved without appealing to additional set-theoretic axioms, the conclusion of the latter theorem relies on the Continuum Hypothesis and it is independent of the standard axioms of set theory. We also prove that in the category of C^* -algebras, tensoring with the C^* -algebra of all continuous functions on the Cantor space preserves elementary equivalence. As a side note, neither the Jiang–Su algebra \mathcal{Z} nor any UHF algebra share this property.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.008 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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".