Almost real closed fields with real analytic structure
Why this work is in the frame
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Bibliographic record
Abstract
Cluckers and Lipshitz showed that real closed fields equipped with real analytic structure are o-minimal. This generalizes the well-known subanalytic structure [Formula: see text] on the real numbers. We extend this line of research by investigating ordered fields with real analytic structure that are not necessarily real closed. When considered in a language with a symbol for a convex valuation ring, these structures turn out to be tame as valued fields: we prove that they are [Formula: see text]-h-minimal. Additionally, our approach gives a precise description of the induced structure on the residue field and the value group, and naturally leads to an Ax–Kochen–Ersov-theorem for fields with real analytic structure.
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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 | 0.001 |
| 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) | 0.001 | 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 it