Bibliographic record
Abstract
this paper, we analyze the structure of the Hardy fields associated with o-minimal expansions of the reals with exponential function. In fact, we work in the following more general setting. We take T to be the theory of a polynomially bounded o-minimal expansion P of the ordered field of real numbers by a set F T of real-valued functions. We assume that F T contains a symbol for every 0-definable function. Further, we assume that T defines the restricted exponential and logarithmic functions (cf. [D--M--M1]). Then also T(exp) is o-minimal (cf. [D--S2]). Here, T(exp) denotes the theory of the expansion (P; exp) where exp is the un-restricted real exponential function. Finally, we take any model R of T(exp) which contains (R; +; \\Delta; !; F T ; exp) as a substructure. Then we consider the Hardy field H(R) (see Section 2.2 for the definition) as a field equipped with convex valuations. Under the given assumptions, it is equal to the closure LER;F T (x) of its subfield R(x) under F T , exp and its inverse log; here, x denotes the germ of the identity function. We analyze its valuation theoretical structure by explicitly showing how LER;F T (x) can be built up (cf. Section 3.3). Our construction method yields the following result (see Section 3.4 for definitions):
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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 | 0.001 | 0.000 |
| 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) | 0.001 | 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 teacher head, 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".