CONSTRUCTING TYPES IN DIFFERENTIALLY CLOSED FIELDS THAT ARE ANALYSABLE IN THE CONSTANTS
Bibliographic record
Abstract
Abstract Analysability of finiteU-rank types are explored both in general and in the theory ${\rm{DC}}{{\rm{F}}_0}$ . The well-known fact that the equation $\delta \left( {{\rm{log}}\,\delta x} \right) = 0$ is analysable in but not almost internal to the constants is generalized to show that $\underbrace {{\rm{log}}\,\delta \cdots {\rm{log}}\,\delta }_nx = 0$ is not analysable in the constants in $\left( {n - 1} \right)$ -steps. The notion of acanonical analysisis introduced–-namely an analysis that is of minimal length and interalgebraic with every other analysis of that length. Not every analysable type admits a canonical analysis. Using properties of reductions and coreductions in theories with the canonical base property, it is constructed, for any sequence of positive integers $\left( {{n_1}, \ldots ,{n_\ell }} \right)$ , a type in ${\rm{DC}}{{\rm{F}}_0}$ that admits a canonical analysis with the property that theith step hasU-rank ${n_i}$ .
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".