Why this work is in the frame
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Bibliographic record
Abstract
Recall that a map T \\colon C(X,E) \\to C(Y,F), where X, Y are Tychonoff spaces and E, F are normed spaces, is said to be separating, if for any 2 functions f,g \\in C(X,E) we have c(T(f)) \\cap c(T(g))= \\varnothing provided c(f) \\cap c(g) = \\varnothing. Here c(f) is the co-zero set of f. A typical result generalizing the Banach--Stone theorem is of the following type (established by Araujo): if T is bijective and additive such that both T and T-1 are separating, then the realcompactification n X of X is homeomorphic to n Y. In this paper we show that a similar result is true if additivity is replaced by subadditivity (a map T is called subadditive if ||T(f+g)(y)|| \\leq ||T(f)(y)||+ ||T(g)(y)|| for any f,g \\in C(X,E) and any y \\in Y). Here is our main result (a stronger version is actually established): if T \\colon C(X,E) \\to C(Y,F) is a separating subadditive map, then there exists a continuous map SY\\colon b Y \\rightarrow b X. Moreover, SY is surjective provided T(f)=0 iff f=0. In particular, when T is a bijection such that both T and T-1 are separating and subadditive, b X is homeomorphic to b Y. We also provide an example of a biseparating subadditive map from C(R) onto C(R), which is not additive.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it