Bibliographic record
Abstract
Abstract To each computable enumerable (c.e.) setAwith a particular enumeration {As}s∈ωthere is associated a settling functionmA(x), wheremA(x) is the last stage when a number less than or equal toxwas enumerated intoA. One c.e. setAis settling time dominated by another setB(B>stA) if for every computable functionf, for all but finitely manyx, mB(x) >f(mA(x)). This settling-time ordering, which is a natural extension to an ordering of the idea of domination, was first introduced by Nabutovsky and Weinberger in [3] and Soare [6]. They desired a sequence of sets descending in this relationship to give results in differential geometry. In this paper we examine properties of the <stordering. We show that it is not invariant under computable isomorphism, that any countable partial ordering embeds into it. that there are maximal and minimal sets, and that two c.e. sets need not have an inf or sup in the ordering. We also examine a related ordering, the strong settling-time ordering where we require for all computablefandg, for almost allx, mB(x) >f(mA(g(x))).
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".