Bibliographic record
Abstract
Abstract It is known that any non-archimedean Fréchet space of countable type is isomorphic to a subspace of . In this paper we prove that there exists a non-archimedean Fréchet space U with a basis ( u n ) such that any basis ( x n ) in a non-archimedean Fréchet space X is equivalent to a subbasis ( u k n ) of ( u n ). Then any non-archimedean Fréchet space with a basis is isomorphic to a complemented subspace of U . In contrast to this, we show that a non-archimedean Fréchet space X with a basis ( x n ) is isomorphic to a complemented subspace of if and only if X is isomorphic to one of the following spaces: c 0 , c 0 × . Finally, we prove that there is no nuclear non-archimedean Fréchet space H with a basis ( h n ) such that any basis ( y n ) in a nuclear non-archimedean Fréchet space Y is equivalent to a subbasis ( h k n ) of ( h n ).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.007 | 0.007 |
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; both teacher heads agree on what is shown here.
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".