Bibliographic record
Abstract
Let A \mathcal {A} be a mathematical structure with an additional relation R R . We are interested in the degree spectrum of R R , either among computable copies of A \mathcal {A} when ( A , R ) (\mathcal {A},R) is a “natural” structure, or (to make this rigorous) among copies of ( A , R ) (\mathcal {A},R) computable in a large degree d . We introduce the partial order of degree spectra on a cone and begin the study of these objects. Using a result of Harizanov—that, assuming an effectiveness condition on A \mathcal {A} and R R , if R R is not intrinsically computable, then its degree spectrum contains all c.e. degrees—we see that there is a minimal non-trivial degree spectrum on a cone, consisting of the c.e. degrees. We show that this does not generalize to d.c.e. degrees by giving an example of two incomparable degree spectra on a cone. We also give a partial answer to a question of Ash and Knight: they asked whether (subject to some effectiveness conditions) a relation which is not intrinsically Δ α 0 \Delta ^0_\alpha must have a degree spectrum which contains all of the α \alpha -CEA degrees. We give a positive answer to this question for α = 2 \alpha = 2 by showing that any degree spectrum on a cone which strictly contains the Δ 2 0 \Delta ^0_2
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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".